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13 Questions

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If the sum of three numbers in geometric progression is $13$ and the sum of their individual squares is $91$, then what are the three numbers? [closed]

sequences-and-series

Aug 31 '16 at 19:01 jimpix 257

votes

answer

views

For a series in geometric progression, if $t_3 = 20$ and $t_7 = 320$, then what is the value of $a=t_{1}$, the common ratio $r$ and $t_{10}$? [closed]

sequences-and-series

Aug 31 '16 at 19:02 jimpix 257

-2

votes

answers

722

views

What is the value of $\sum_{r = 1}^{89}{\log_{10}(\tan \:r)}$, where $r$ is measured in degrees? [closed]

sequences-and-series logarithms

Oct 17 '16 at 11:05 jimpix 257

votes

answer

views

How do I develop intuition for solving determinant problems?

determinant

Aug 21 '16 at 17:06 Michael Hardy 249k

votes

answers

151

views

How do I show that $2q^2 = 9pr$ if one root of the equation $px^2 + qx + r = 0$ is double the other?

quadratics

Aug 21 '16 at 5:43 Anonymous_original 133

votes

answer

views

If the $4$th and $7$th terms of a Harmonic Progression are $\frac{2}{3}$ and $\frac{2}{5}$, then what is the first and $n$th term?

sequences-and-series

Aug 18 '16 at 5:57 Community♦ 1

votes

answer

196

views

Why does $f_{1}(n) = 10n^3 + 5n^2 + 17 \in \theta(n^3)$? [closed]

asymptotics

Aug 17 '16 at 9:16 Community♦ 1

vote

answers

298

views

Why is the formula for the sum of infinite terms of a geometric progression only defined for $r < 1$? [duplicate]

sequences-and-series

Aug 13 '16 at 11:55 paf 4,270

votes

answers

views

What is the solution of this quadratic equation problem?

quadratics

Aug 12 '16 at 9:26 jimpix 257

votes

answers

173

views

How is the Euclidean Algorithm used to solve IMO 1959 Problem 1?

euclidean-algorithm

Aug 21 '16 at 6:10 A---B 3,342

votes

answers

125

views

If $x^a$ is $x$ multiplied $a$ times, then how does $x^{-1}$ make sense?

exponentiation

Aug 7 '16 at 15:40 quid♦ 39.6k

votes

answers

views

What is the square root of $3 + 2\sqrt{10}i$?

complex-numbers

Aug 6 '16 at 16:59 Community♦ 1

-1

votes

answer

views

Why is ${(i^{4})}^{2n}$ = 1?

complex-numbers

Aug 3 '16 at 9:14 hmakholm left over Monica 268k

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13 Questions

If the sum of three numbers in geometric progression is $13$ and the sum of their individual squares is $91$, then what are the three numbers? [closed]

For a series in geometric progression, if $t_3 = 20$ and $t_7 = 320$, then what is the value of $a=t_{1}$, the common ratio $r$ and $t_{10}$? [closed]

What is the value of $\sum_{r = 1}^{89}{\log_{10}(\tan \:r)}$, where $r$ is measured in degrees? [closed]

How do I develop intuition for solving determinant problems?

How do I show that $2q^2 = 9pr$ if one root of the equation $px^2 + qx + r = 0$ is double the other?

If the $4$th and $7$th terms of a Harmonic Progression are $\frac{2}{3}$ and $\frac{2}{5}$, then what is the first and $n$th term?

Why does $f_{1}(n) = 10n^3 + 5n^2 + 17 \in \theta(n^3)$? [closed]

Why is the formula for the sum of infinite terms of a geometric progression only defined for $r < 1$? [duplicate]

What is the solution of this quadratic equation problem?

How is the Euclidean Algorithm used to solve IMO 1959 Problem 1?

If $x^a$ is $x$ multiplied $a$ times, then how does $x^{-1}$ make sense?

What is the square root of $3 + 2\sqrt{10}i$?

Why is ${(i^{4})}^{2n}$ = 1?