User Hardy - Mathematics Stack Exchange

bio	website	google.com
	location	Melbourne, Australia
	age	30
visits	member for	1 year, 3 months
	seen	May 18 at 18:49
stats	profile views	489

	1,190 reputation	bio	website	google.com	visits	member for	1 year, 3 months
1624 badges		location	Melbourne, Australia		seen	May 18 at 18:49

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256

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Showing that $\cos n\pi\theta$ is periodic unless $\theta$ is an even integer.

jun 24 '12 at 18:35 Community♦ 1

3

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2

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72

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question about binomial expansion's coefficients

real-analysis sequences-and-series trigonometry complex-numbers

apr 20 '12 at 23:36 GarouDan 1,346

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4

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1

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117

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Summing an unusual series: $\frac {x} {2!(n-2)!}+\frac {x^{2}} {5!(n-5)!}+\dots +\frac {x^{\frac{n}{3}}} {(n-1)!}$

real-analysis sequences-and-series

apr 19 '12 at 23:32 Aryabhata 47.5k

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5

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2

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193

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Primitive roots of unity

real-analysis elementary-number-theory complex-numbers

apr 19 '12 at 20:46 Jyrki Lahtonen 30.7k

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1

answer

80

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Is there a forumla for number of primes preceding a natural number?

real-analysis elementary-number-theory prime-numbers complex-numbers

apr 17 '12 at 23:07 Greg Martin 7,643

1

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2

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79

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Showing $2x=\left( 2n+1\right) \pi \left( 1-\cos x\right) $ has $2n+3$ roots when $n\in \mathbb{Z}_+$

algebra-precalculus trigonometry roots

apr 14 '12 at 9:23 Did 102k

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0

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73

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Differentiation of Generic Riemann integrals

real-analysis integration

apr 6 '12 at 20:08 Hardy 1,190

2

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1

answer

88

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Computing a limit which i suspect should evaluate to $\dfrac{\sin x}{x}$

real-analysis limit

apr 5 '12 at 21:24 Aryabhata 47.5k

4

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4

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135

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computing a trignometric limit

real-analysis sequences-and-series limit

apr 5 '12 at 22:22 Hardy 1,190

2

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0

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88

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Another Question based on Abel's theorem of multiplication of series

real-analysis sequences-and-series convergence

mar 25 '12 at 19:57 Hardy 1,190

3

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2

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286

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Behaviour of $\sum u_{n}\cos(n\theta +a) $ when $\theta\over\pi$ is rational and when irrational

real-analysis sequences-and-series limit convergence

mar 27 '12 at 8:35 Julián Aguirre 14.6k

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1

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197

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Question based on Abel's theorem of multiplication of series

real-analysis sequences-and-series limit convergence

mar 24 '12 at 22:27 KCd 5,920

4

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2

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268

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Absolute and uniform convergence of $\sum _{n=1}^{n=\infty }2^{n}\sin \frac {1} {3^{n}z}$

real-analysis sequences-and-series limit convergence

mar 23 '12 at 22:03 Brian M. Scott 154k

2

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1

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123

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Computing $\lim\limits_{m\to \infty }\sum _{n=1}^{m }\frac{z^{m} -1}{( z-1) ^{2}( z^{m+1}-1) }=\frac{1}{( 1-z) ^{2}}$

real-analysis sequences-and-series limit convergence

mar 21 '12 at 20:54 Arturo Magidin 158k

1

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2

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66

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homogeneous linear differential equation question

integral integration integral-equations

mar 22 '12 at 8:32 Thomas Rot 2,081

1

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1

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130

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Uniform convergence of $\sum _{n=1}^{\infty }-2\left( n-1\right) ^{2}x e^{-\left( n-1\right) ^{2}x^{4}}+2n^{2}xe^{-n^{2}x^{2}}\left( x\right)$

real-analysis sequences-and-series convergence proof-strategy

mar 20 '12 at 19:37 Robert Israel 86.3k

1

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1

answer

121

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Rate of Loan Principal being repaid function evaluation

differential-equations mathematical-modeling

mar 20 '12 at 0:55 Henry 32.1k

1

3

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1

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321

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Mathematics From Futurama

differential-equations puzzle recreational-mathematics mathematical-modeling

mar 19 '12 at 18:58 alex.jordan 8,804

3

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3

answers

72

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Absolute convergence of $\sum \dfrac {1} {\left( m_{1}^{2}+m_{2}^{2}+\ldots +m_{r }^{2}\right)^{\mu} } $

real-analysis sequences-and-series convergence proof-strategy

mar 17 '12 at 20:09 Eric 33.3k

2

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1

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111

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$x+\sum _{i=2}^{i=n}\left(x^{\left(2i-1\right) ^{-1}}-x^{\left( 2i-3\right) ^{-1}}\right) = ?$

real-analysis sequences-and-series limit convergence

mar 17 '12 at 2:33 Byron Schmuland 15.4k

0

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1

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45

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Validation of partial sum $\sum _{i=1}^{i=n}\dfrac {x} {\left( \left( i-1\right) x+1\right) \left( ix+1\right) }=1-\dfrac {1} {nx+1}$

real-analysis sequences-and-series

mar 15 '12 at 19:43 quartz 859

0

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0

answers

112

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Linearity property of Mathematical objects

linear-algebra probability vector-spaces

mar 14 '12 at 5:40 Hardy 1,190

1

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1

answer

141

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Inequality proof by induction

algebra-precalculus proof-strategy

mar 13 '12 at 21:02 Hardy 1,190

26

44

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6

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2

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What made you choose your research field?

soft-question advice

dec 12 at 5:14 Kyle 1,485

5

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1

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373

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Proof of a theorem of Cauchy's on the convergence of an infinite product

real-analysis sequences-and-series convergence proof-strategy

mar 12 '12 at 22:13 Aryabhata 47.5k

3

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1

answer

109

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Convergence of $\prod\limits_{n=0}^\infty ( 1+u_{n}) $ when $\sum\limits_{n=0}^{\infty }u_{n}$ and $\sum \limits_{n=0}^\infty u_{n}^{2}$ diverge

real-analysis sequences-and-series limit convergence

mar 12 '12 at 2:39 anon 39.8k

1

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2

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79

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Sums of Double series where $a_{m,n}=\dfrac {m-n} {2^{m+n}}\dfrac {\left( m+n-1\right) !} {m!n!}$

real-analysis sequences-and-series convergence

mar 12 '12 at 0:10 Fabian 10.7k

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2

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1

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73

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Convergence of $q_{1}+q_{1}^{2}+q_{2}^{3}+q_{1}^{4}+q_{2}^{5}+q_{3}^{6}+q_{1}^{7}+\ldots$

real-analysis number-theory sequences-and-series limit

mar 11 '12 at 22:20 user17762 76.1k

0

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2

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101

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Absolute convergence for all values except the values $z=\left( 1+\frac {a} {m}\right) e^{\frac {2k\pi i} {m}}$

real-analysis sequences-and-series complex-analysis limit convergence

mar 11 '12 at 19:47 Martin Argerami 16.9k

4

8

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4

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297

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Trying to show $1-\dfrac {1} {2} -\dfrac {1} {4}+\dfrac {1} {3}-\dfrac {1} {6}-\dfrac {1} {8}+\dfrac {1} {5}-\cdots =\dfrac {1} {2}\log 2$

real-analysis combinatorics sequences-and-series

mar 11 '12 at 21:19 Hardy 1,190

Hardy

105 Questions