Question

Find a formula for $1 + 3 + 5 + ... +(2n - 1)$, for $n \ge 1$, and prove that your formula is correct.

score 39.1k · Answer 1 · 2026-04-03 11:49:50

39.1k

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Find a formula for $1 + 3 + 5 + ... +(2n - 1)$, for $n \ge 1$, and prove that your formula is correct.

Published on 03 Apr 2026 - 11:49

score 120 · Answer 2 · 2026-03-25 07:45:59

120

Views

Let $a,b,c>0$ such $ \frac{b+c}{a}+ \frac{c+a}{b}+ \frac{a+b}{c} = 2\left(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ac} \right)$

Published on 25 Mar 2026 - 7:45

score 54 · Answer 3 · 2026-04-09 18:40:57

54

Views

Finding an exact solution to a difference equation

Published on 09 Apr 2026 - 18:40

score 282 · Answer 4 · 2026-04-10 04:10:48

282

Views

Combinatorial proof involving reciprocals

Published on 10 Apr 2026 - 4:10

score 691 · Answer 5 · 2026-04-09 18:30:04

691

Views

What does it mean for a series to be convergent?

Published on 09 Apr 2026 - 18:30

score 626 · Answer 6 · 2026-04-11 07:20:56

626

Views

Recurrence Relation Solving Problem

Published on 11 Apr 2026 - 7:20

score 392 · Answer 7 · 2026-04-12 19:55:30

392

Views

simplifying a triple sum of products of binomial coefficients

Published on 12 Apr 2026 - 19:55

score 545 · Answer 8 · 2026-04-09 15:12:20

545

Views

Converting failure rates between periods

Published on 09 Apr 2026 - 15:12

score 106 · Answer 9 · 2014-05-28 17:36:52

106

Views

Sum of eight even integers that cannot be repeated more than twice is $50$

Published on 28 May 2014 - 17:36

score 1.1k · Answer 10 · 2026-04-12 22:12:48

1.1k

Views

Sum of potencies with higher potency as clue

Published on 12 Apr 2026 - 22:12

score 265 · Answer 11 · 2026-03-28 16:58:13

265

Views

Why is $\sum\limits_{k=0}^{n}(-1)^k\binom{n}{k}^2=(-1)^{n/2}\binom{n}{n/2}$ if $n$ is even?

Published on 28 Mar 2026 - 16:58

score 1.6k · Answer 12 · 2026-04-10 17:56:23

1.6k

Views

Is the integral test not valid for negative, upwards-trending functions?

Published on 10 Apr 2026 - 17:56

score 216 · Answer 13 · 2026-04-12 21:51:50

216

Views

How find this sum $S(x)=\sum_{k=1}^{\infty}\frac{\cos{(2kx\pi)}}{k}$

Published on 12 Apr 2026 - 21:51

score 65 · Answer 14 · 2026-04-12 04:14:32

65

Views

How find this sum $S=\sum_{i=1}^{m}(-1)^{a_{i}}\cdot 2^{m-i}$ and $2^i\equiv a_{i}\pmod n$

Published on 12 Apr 2026 - 4:14

score 92 · Answer 15 · 2026-04-03 13:25:00

92

Views

$\sum_{k=0}^{n}(-1)^k {{m+1}\choose{k}}{{m+n-k}\choose{m}}$

Published on 03 Apr 2026 - 13:25

List Question

Find a formula for $1 + 3 + 5 + ... +(2n - 1)$, for $n \ge 1$, and prove that your formula is correct.

Let $a,b,c>0$ such $ \frac{b+c}{a}+ \frac{c+a}{b}+ \frac{a+b}{c} = 2\left(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ac} \right)$

Finding an exact solution to a difference equation

Combinatorial proof involving reciprocals

What does it mean for a series to be convergent?

Recurrence Relation Solving Problem

simplifying a triple sum of products of binomial coefficients

Converting failure rates between periods

Sum of eight even integers that cannot be repeated more than twice is $50$

Sum of potencies with higher potency as clue

Why is $\sum\limits_{k=0}^{n}(-1)^k\binom{n}{k}^2=(-1)^{n/2}\binom{n}{n/2}$ if $n$ is even?

Is the integral test not valid for negative, upwards-trending functions?

How find this sum $S(x)=\sum_{k=1}^{\infty}\frac{\cos{(2kx\pi)}}{k}$

How find this sum $S=\sum_{i=1}^{m}(-1)^{a_{i}}\cdot 2^{m-i}$ and $2^i\equiv a_{i}\pmod n$

$\sum_{k=0}^{n}(-1)^k {{m+1}\choose{k}}{{m+n-k}\choose{m}}$

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