Question

Do these converge?

score 64 · Answer 1 · 2026-04-14 18:30:06

64

Views

Do these converge?

Published on 14 Apr 2026 - 18:30

score 187 · Answer 2 · 2026-04-14 23:29:31

187

Views

For which of the following choice of $a_k$ is $\sum a_k$ convergent?

Published on 14 Apr 2026 - 23:29

score 234 · Answer 3 · 2026-04-17 10:14:39

234

Views

Prove $1 + \frac{1}{4} + \frac{1}{9} + \cdots + \frac{1}{n^2} < 2 - \frac{1}{n}$ by Induction

Published on 17 Apr 2026 - 10:14

score 90 · Answer 4 · 2026-04-15 12:46:35

90

Views

Use mathematical induction to prove $\sum_{i=1}^{n}(2i+4)=n^2+5n$

Published on 15 Apr 2026 - 12:46

score 87 · Answer 5 · 2026-04-11 02:02:58

87

Views

What is the substitution to remove integration limit from inside an integral?

Published on 11 Apr 2026 - 2:02

score 94 · Answer 6 · 2026-04-14 04:57:55

94

Views

What is the sum of infinte values of x, where x tends to zero? Is the sum 0, or does it go on to become infinite?

Published on 14 Apr 2026 - 4:57

score 281 · Answer 7 · 2026-04-14 08:55:53

281

Views

to find total number of subsets

Published on 14 Apr 2026 - 8:55

score 291 · Answer 8 · 2026-04-14 00:44:06

291

Views

Compute the following sum $ \sum_{i=0}^{n} \binom{n}{i}(i+1)^{i-1}(n - i + 1) ^ {n - i - 1}$?

Published on 14 Apr 2026 - 0:44

score 186 · Answer 9 · 2026-04-17 03:33:57

186

Views

Calculate the sum : $S=1+\frac{\sin x}{\sin x}+\frac{\sin2x}{\sin^2 x}+\cdots +\frac{\sin nx}{\sin^n x}$

Published on 17 Apr 2026 - 3:33

score 64 · Answer 10 · 2026-04-16 13:17:57

64

Views

Inverse of $f(x) = \sum_{i=0}^x \lfloor 2 \pi i \rfloor$

Published on 16 Apr 2026 - 13:17

score 86 · Answer 11 · 2026-04-18 23:34:59

86

Views

When does equality hold in $\bigg(\sum_{k=1}^na_k^2\bigg)\bigg(\sum_{k=1}^nb_k^2\bigg)\ge\bigg(\sum_{k=1}^na_kb_k\bigg)^2$

Published on 18 Apr 2026 - 23:34

score 215 · Answer 12 · 2026-04-11 19:47:39

215

Views

Summation notation for divided factorial.

Published on 11 Apr 2026 - 19:47

score 184 · Answer 13 · 2026-04-15 09:32:33

184

Views

Prove that $\lim_{n\rightarrow\infty}\frac{1}{n^{p+1}}\sum_{k=1}^{n}k^{p}=\frac{1}{p+1} $

Published on 15 Apr 2026 - 9:32

score 141 · Answer 14 · 2026-04-09 02:07:43

141

Views

Does grouping the terms of a series (but not moving them) change the sum?

Published on 09 Apr 2026 - 2:07

score 99 · Answer 15 · 2026-04-15 17:58:58

99

Views

Proof by induction of the formula for $2^0+2^1+2^2+...+2^n$?

Published on 15 Apr 2026 - 17:58

List Question

Do these converge?

For which of the following choice of $a_k$ is $\sum a_k$ convergent?

Prove $1 + \frac{1}{4} + \frac{1}{9} + \cdots + \frac{1}{n^2} < 2 - \frac{1}{n}$ by Induction

Use mathematical induction to prove $\sum_{i=1}^{n}(2i+4)=n^2+5n$

What is the substitution to remove integration limit from inside an integral?

What is the sum of infinte values of x, where x tends to zero? Is the sum 0, or does it go on to become infinite?

to find total number of subsets

Compute the following sum $ \sum_{i=0}^{n} \binom{n}{i}(i+1)^{i-1}(n - i + 1) ^ {n - i - 1}$?

Calculate the sum : $S=1+\frac{\sin x}{\sin x}+\frac{\sin2x}{\sin^2 x}+\cdots +\frac{\sin nx}{\sin^n x}$

Inverse of $f(x) = \sum_{i=0}^x \lfloor 2 \pi i \rfloor$

When does equality hold in $\bigg(\sum_{k=1}^na_k^2\bigg)\bigg(\sum_{k=1}^nb_k^2\bigg)\ge\bigg(\sum_{k=1}^na_kb_k\bigg)^2$

Summation notation for divided factorial.

Prove that $\lim_{n\rightarrow\infty}\frac{1}{n^{p+1}}\sum_{k=1}^{n}k^{p}=\frac{1}{p+1} $

Does grouping the terms of a series (but not moving them) change the sum?

Proof by induction of the formula for $2^0+2^1+2^2+...+2^n$?

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