User Thomas Finley

12 votes

4 answers

534 views

Problem when proving the series $1+\frac 13-\frac 12+\frac 15+\frac17-\frac 14 +\frac 19+\frac 1{11}-\frac 16+...$ converges to $\frac 32\log 2.$

asked Jun 16, 2023 at 5:41

10 votes

5 answers

871 views

Test the convergence of the series $1+\frac{2^2}{3^2}+\frac{2^2.4^2}{3^2.5^2}+\frac{2^2.4^2.6^2}{3^2.5^2.7^2}+\cdots$

asked Jun 15, 2023 at 10:09

7 votes

1 answer

300 views

Strange Absurdities in a Calculus Problem!

asked May 13, 2023 at 7:55

7 votes

3 answers

639 views

Understanding definition of a continuous random variable

asked Jul 26 at 18:53

6 votes

6 answers

571 views

Population of a city doubles in $50$ years. In how many years will it triple?

asked May 12, 2023 at 7:26

6 votes

3 answers

1k views

Solve the following differential equation $x^2\frac{d^2y}{dx^2}+4x\frac{dy}{dx}+2y=e^x.$

asked Jun 19, 2023 at 16:30

6 votes

1 answer

738 views

Doesn't an integral domain automatically imply that is it is of characteristic zero?

asked Jul 23, 2023 at 16:48

5 votes

2 answers

286 views

Trouble in Proving the Sequential Criterion for Limits at Infinity

asked Aug 26, 2023 at 7:25

5 votes

1 answer

201 views

Let $f:[0,1]\to \Bbb R$ such that $f(x)=x$ if $x$ be rational $x^2$ if $x$ be irrational. Find $\underline{\int}_0^1 f$ and $\overline{\int}_0^1f.$

asked Feb 13 at 3:45

5 votes

1 answer

97 views

Show that $\int_0^1\frac{1}{(x+1)(x+2)\sqrt {x(1-x)}}$ is convergent.

asked Jun 6 at 15:51

4 votes

3 answers

595 views

A strange confusion over a problem of continuity in Multivariate Calculus.

asked May 7 at 3:40

4 votes

0 answers

109 views

Deduce, the Taylor series expansion of $\arcsin x$ from the Taylor Series expansion of $e^{a\arcsin x}$

asked Sep 24, 2023 at 5:39

4 votes

2 answers

287 views

Let $S = \{m + n\sqrt 2 : m, n \in\mathbb Z\}$ Prove that $S$ is dense in $\Bbb R.$

asked Jun 9, 2023 at 4:33

3 votes

0 answers

208 views

Show that $[0,1]$ and $[0,1]\times [0,1]$ have the same cardinality.

asked Jun 12, 2023 at 16:55

3 votes

1 answer

83 views

Let $P(x)=b_0+b_1x+\cdots+b_rx^r$ be a polynomial with real coefficients.Prove that the graph of $P(x)$ cuts the x-axis at the origin iff $m$ is odd.

asked May 13, 2023 at 16:24

3 votes

1 answer

128 views

Prove that $\Bbb R$ is uncountable

asked May 28, 2023 at 17:44

3 votes

2 answers

112 views

Prove the existence of $\sqrt b$ for any real number $b\geq 0.$

asked May 29, 2023 at 7:03

3 votes

2 answers

151 views

If $A \subseteq B$ and $B$ is countable, then $A$ is either countable, finite, or empty.

asked May 29, 2023 at 16:23

3 votes

1 answer

211 views

If $A_n$ is a countable set for each $n ∈ \Bbb N,$ then $\cup_{n=1}^{\infty}A_n,$ is countable.

asked May 30, 2023 at 9:12

3 votes

1 answer

61 views

Can this solution of a Ring Theory problem be improved? [duplicate]

asked Jul 29, 2023 at 6:59

3 votes

2 answers

185 views

Any Strategies to Factorise Expressions (, Faster)?

asked Jun 19, 2023 at 11:09

3 votes

1 answer

51 views

Let $f$ be a function such that $g(y)=\sup_{x\in \Bbb{R}} [xy-f(x)]$ is finite. Show that $f$ satisfies $\lim_{|x|\to\infty}\frac{f(x)}{|x|}=\infty.$

asked Oct 25, 2023 at 11:45

3 votes

2 answers

410 views

Let $V$ be a vector space over $C$ with dimension $n.$ Prove that if $V$ is now regarded as a vector space over $R,$ then $\dim V =2n.$

asked Oct 27, 2023 at 11:23

3 votes

2 answers

318 views

Need help in understanding how two linear transformations are the same in Linear Algebra.

asked Nov 17, 2023 at 3:07

3 votes

1 answer

87 views

Is it justified to derive a formula of a mapping $T$ by assuming $T$ to be linear transformation?

asked Nov 17, 2023 at 8:12

3 votes

1 answer

65 views

Find the volume of the solid inside the cylinder $x^2+y^2-2ay=0$ and between $z=0$ and the paraboloid $4az=x^2+y^2$ equals $\frac{3\pi a^3}{8}.$

asked Jun 23 at 15:26

3 votes

1 answer

96 views

Problem in understanding the unique factorization theorem for Euclidean Rings.

asked Feb 3 at 9:43

3 votes

6 answers

332 views

Why am I getting two different answers when the countour integral is performed in two different ways?

asked Sep 4 at 18:59

2 votes

0 answers

38 views

Clarification needed regarding the definition of a genral solution of a first order PDE.

asked Jul 28 at 7:10

2 votes

0 answers

79 views

Why does the volume comes out to be $\pi\frac{a^3}{8}$ instead of $\frac{3\pi a^3}{8}$?

asked Jun 24 at 16:29

Stack Exchange Network

213 Questions

Problem when proving the series $1+\frac 13-\frac 12+\frac 15+\frac17-\frac 14 +\frac 19+\frac 1{11}-\frac 16+...$ converges to $\frac 32\log 2.$

Test the convergence of the series $1+\frac{2^2}{3^2}+\frac{2^2.4^2}{3^2.5^2}+\frac{2^2.4^2.6^2}{3^2.5^2.7^2}+\cdots$

Strange Absurdities in a Calculus Problem!

Understanding definition of a continuous random variable

Population of a city doubles in $50$ years. In how many years will it triple?

Solve the following differential equation $x^2\frac{d^2y}{dx^2}+4x\frac{dy}{dx}+2y=e^x.$

Doesn't an integral domain automatically imply that is it is of characteristic zero?

Trouble in Proving the Sequential Criterion for Limits at Infinity

Let $f:[0,1]\to \Bbb R$ such that $f(x)=x$ if $x$ be rational $x^2$ if $x$ be irrational. Find $\underline{\int}_0^1 f$ and $\overline{\int}_0^1f.$

Show that $\int_0^1\frac{1}{(x+1)(x+2)\sqrt {x(1-x)}}$ is convergent.

A strange confusion over a problem of continuity in Multivariate Calculus.

Deduce, the Taylor series expansion of $\arcsin x$ from the Taylor Series expansion of $e^{a\arcsin x}$

Let $S = \{m + n\sqrt 2 : m, n \in\mathbb Z\}$ Prove that $S$ is dense in $\Bbb R.$

Show that $[0,1]$ and $[0,1]\times [0,1]$ have the same cardinality.

Let $P(x)=b_0+b_1x+\cdots+b_rx^r$ be a polynomial with real coefficients.Prove that the graph of $P(x)$ cuts the x-axis at the origin iff $m$ is odd.

Prove that $\Bbb R$ is uncountable

Prove the existence of $\sqrt b$ for any real number $b\geq 0.$

If $A \subseteq B$ and $B$ is countable, then $A$ is either countable, finite, or empty.

If $A_n$ is a countable set for each $n ∈ \Bbb N,$ then $\cup_{n=1}^{\infty}A_n,$ is countable.

Can this solution of a Ring Theory problem be improved? [duplicate]

Any Strategies to Factorise Expressions (, Faster)?

Let $f$ be a function such that $g(y)=\sup_{x\in \Bbb{R}} [xy-f(x)]$ is finite. Show that $f$ satisfies $\lim_{|x|\to\infty}\frac{f(x)}{|x|}=\infty.$

Let $V$ be a vector space over $C$ with dimension $n.$ Prove that if $V$ is now regarded as a vector space over $R,$ then $\dim V =2n.$

Need help in understanding how two linear transformations are the same in Linear Algebra.

Is it justified to derive a formula of a mapping $T$ by assuming $T$ to be linear transformation?

Find the volume of the solid inside the cylinder $x^2+y^2-2ay=0$ and between $z=0$ and the paraboloid $4az=x^2+y^2$ equals $\frac{3\pi a^3}{8}.$

Problem in understanding the unique factorization theorem for Euclidean Rings.

Why am I getting two different answers when the countour integral is performed in two different ways?

Clarification needed regarding the definition of a genral solution of a first order PDE.

Why does the volume comes out to be $\pi\frac{a^3}{8}$ instead of $\frac{3\pi a^3}{8}$?