Question

Infinite summation $\sum_\limits{n=0}^\infty \frac{\sin(n\theta)}{2^n}$

score 1.2k · Answer 1 · 2019-01-01 23:29:47

1.2k

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Infinite summation $\sum_\limits{n=0}^\infty \frac{\sin(n\theta)}{2^n}$

Published on 01 Jan 2019 - 23:29

score 95 · Answer 2 · 2026-03-27 02:07:07

95

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Is there a generalized way to find an inverse of a function defined as a sum (if the inverse exists)?

Published on 27 Mar 2026 - 2:07

score 74 · Answer 3 · 2019-01-02 16:15:44

74

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If $|f(p+q)-f(q)|\leq p/q$ for rational $p$ and $q$ (with $q\neq 0$), then $\sum_{i=0}^k |f(2^k) -f(2^i)| \leq k(k-1)/2$

Published on 02 Jan 2019 - 16:15

score 52 · Answer 4 · 2026-03-26 04:29:41

52

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Identity involving floor, ceiling and nearest integer functions

Published on 26 Mar 2026 - 4:29

score 818 · Answer 5 · 2026-03-29 03:36:34

818

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Find the $\frac mn$ if $T=\sin 5°+\sin10°+\sin 15°+\cdots+\sin175°=\tan \frac mn$

Published on 29 Mar 2026 - 3:36

score 75 · Answer 6 · 2019-01-02 21:41:04

75

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If $ \sum\limits_{n=1}^{N} a_n r_n=0$, what can we say about $ \sum\limits_{n=1}^{N} a_n (r_n)^2=0$

Published on 02 Jan 2019 - 21:41

score 74 · Answer 7 · 2026-03-25 06:06:17

74

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Is there a way to sum (part of) the harmonic series to a given total?

Published on 25 Mar 2026 - 6:06

score 191 · Answer 8 · 2026-03-26 04:32:23

191

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Double sum over $\left\lfloor{ac+bd\over k}\right\rfloor$

Published on 26 Mar 2026 - 4:32

score 67 · Answer 9 · 2019-01-03 22:31:36

67

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An equal expression to $\sum^{z}_{n=0}n\frac{x^{z-n}}{(z-n)!}$

Published on 03 Jan 2019 - 22:31

score 880 · Answer 10 · 2026-03-29 03:36:34

880

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If $\sin 5°+\sin 10°+\sin15°+\cdots+\sin 40°=a$, then $\sin 5°+\sin 10°+\sin15°+\cdots+\sin 175°=?$

Published on 29 Mar 2026 - 3:36

score 269 · Answer 11 · 2026-03-22 10:08:59

269

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Proof That $\sum_{k=1}^{n-1}\int_{k}^{k+1}\left\{x\right\}f´(x)dx=\int_{1}^{n}\left\{x\right\}f´(x)dx$

Published on 22 Mar 2026 - 10:08

score 954 · Answer 12 · 2019-01-04 15:18:53

954

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Evaluate $\sum_{n=2}^\infty \frac{\ln(n)(-1)^n}{n^2} $

Published on 04 Jan 2019 - 15:18

score 2.9k · Answer 13 · 2019-01-04 19:59:12

2.9k

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Index of summation - integer?

Published on 04 Jan 2019 - 19:59

score 111 · Answer 14 · 2019-01-05 07:36:14

111

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Simplification of a Combinatoric problem (n k)^2

Published on 05 Jan 2019 - 7:36

score 100 · Answer 15 · 2019-01-05 13:59:45

100

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Where does my counting argument fails (Counting of numbers with freshness $k$)?

Published on 05 Jan 2019 - 13:59

List Question

Infinite summation $\sum_\limits{n=0}^\infty \frac{\sin(n\theta)}{2^n}$

Is there a generalized way to find an inverse of a function defined as a sum (if the inverse exists)?

If $|f(p+q)-f(q)|\leq p/q$ for rational $p$ and $q$ (with $q\neq 0$), then $\sum_{i=0}^k |f(2^k) -f(2^i)| \leq k(k-1)/2$

Identity involving floor, ceiling and nearest integer functions

Find the $\frac mn$ if $T=\sin 5°+\sin10°+\sin 15°+\cdots+\sin175°=\tan \frac mn$

If $ \sum\limits_{n=1}^{N} a_n r_n=0$, what can we say about $ \sum\limits_{n=1}^{N} a_n (r_n)^2=0$

Is there a way to sum (part of) the harmonic series to a given total?

Double sum over $\left\lfloor{ac+bd\over k}\right\rfloor$

An equal expression to $\sum^{z}_{n=0}n\frac{x^{z-n}}{(z-n)!}$

If $\sin 5°+\sin 10°+\sin15°+\cdots+\sin 40°=a$, then $\sin 5°+\sin 10°+\sin15°+\cdots+\sin 175°=?$

Proof That $\sum_{k=1}^{n-1}\int_{k}^{k+1}\left\{x\right\}f´(x)dx=\int_{1}^{n}\left\{x\right\}f´(x)dx$

Evaluate $\sum_{n=2}^\infty \frac{\ln(n)(-1)^n}{n^2} $

Index of summation - integer?

Simplification of a Combinatoric problem (n k)^2

Where does my counting argument fails (Counting of numbers with freshness $k$)?

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