Question

sum of sequences - proof by induction?

score 122 · Answer 1 · 2026-04-14 20:16:09

122

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sum of sequences - proof by induction?

Published on 14 Apr 2026 - 20:16

score 75 · Answer 2 · 2026-04-08 21:06:11

75

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Proof by inductions method

Published on 08 Apr 2026 - 21:06

score 148 · Answer 3 · 2026-04-17 00:45:14

148

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For all non-negative integers $n$ such that $n ≥ 8$, there exist non-negative integers $a_n$ and $b_n$ such that $3a_n+5b_n = n$

Published on 17 Apr 2026 - 0:45

score 1k · Answer 4 · 2026-04-11 21:29:33

1k

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Inductive proof of symmetric identity of binomial coefficients

Published on 11 Apr 2026 - 21:29

score 147 · Answer 5 · 2026-04-15 13:22:42

147

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Show that $\sum\limits_{k=1}^{n-1} (n-k) x^k$ is non-decreasing for $x \in ]-1,1[$.

Published on 15 Apr 2026 - 13:22

score 173 · Answer 6 · 2026-04-16 07:48:50

173

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Proving the identity ${n \choose k} = {\sum\limits_{m=k-1}^{n-1} {m \choose k-1}}$ by induction over t=n-k

Published on 16 Apr 2026 - 7:48

score 959 · Answer 7 · 2026-04-16 05:34:46

959

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Induction with floor, ceiling $n\le2^k\implies a_n\le3\cdot k2^k+4\cdot2^k-1$ for $a_n=a_{\lfloor\frac{n}2\rfloor}+a_{\lceil\frac{n}2\rceil}+3n+1$

Published on 16 Apr 2026 - 5:34

score 288 · Answer 8 · 2026-04-14 09:36:50

288

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Proving the sum of cubes?

Published on 14 Apr 2026 - 9:36

score 6.1k · Answer 9 · 2026-04-17 01:53:39

6.1k

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If $a_n = \frac{1}{2} (a_{n-1}+a_{n-2})$ prove $a_n=2+4 \left(\frac{-1}{2}\right)^n$ for $n \geq 2$

Published on 17 Apr 2026 - 1:53

score 155 · Answer 10 · 2026-04-17 15:46:53

155

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Let $x_1 = 3, x_{n+1} = \frac{1}{4-x_n}, \text{for } n \geq 1$. Use induction to show that $0 < x_{n+1} < x_n < 4, \forall n \in \mathbb{N}$.

Published on 17 Apr 2026 - 15:46

score 90 · Answer 11 · 2026-04-10 15:28:15

90

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How to prove that this product of functions is bounded?

Published on 10 Apr 2026 - 15:28

score 107 · Answer 12 · 2026-04-13 20:48:05

107

Views

Don't understand an induction solution.

Published on 13 Apr 2026 - 20:48

score 122 · Answer 13 · 2026-04-15 02:35:13

122

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Prove inequality with integer and real variables

Published on 15 Apr 2026 - 2:35

score 591 · Answer 14 · 2026-04-16 18:08:41

591

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Given $a_1=1, a_2=2, a_{n+1}=n(a_n+a_{n-1})$ find the general term

Published on 16 Apr 2026 - 18:08

score 182 · Answer 15 · 2026-04-13 19:01:11

182

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If $a$ can be written as sum of squares of three rational numbers, prove that $a^m$ can be too.

Published on 13 Apr 2026 - 19:01

List Question

sum of sequences - proof by induction?

Proof by inductions method

For all non-negative integers $n$ such that $n ≥ 8$, there exist non-negative integers $a_n$ and $b_n$ such that $3a_n+5b_n = n$

Inductive proof of symmetric identity of binomial coefficients

Show that $\sum\limits_{k=1}^{n-1} (n-k) x^k$ is non-decreasing for $x \in ]-1,1[$.

Proving the identity ${n \choose k} = {\sum\limits_{m=k-1}^{n-1} {m \choose k-1}}$ by induction over t=n-k

Induction with floor, ceiling $n\le2^k\implies a_n\le3\cdot k2^k+4\cdot2^k-1$ for $a_n=a_{\lfloor\frac{n}2\rfloor}+a_{\lceil\frac{n}2\rceil}+3n+1$

Proving the sum of cubes?

If $a_n = \frac{1}{2} (a_{n-1}+a_{n-2})$ prove $a_n=2+4 \left(\frac{-1}{2}\right)^n$ for $n \geq 2$

Let $x_1 = 3, x_{n+1} = \frac{1}{4-x_n}, \text{for } n \geq 1$. Use induction to show that $0 < x_{n+1} < x_n < 4, \forall n \in \mathbb{N}$.

How to prove that this product of functions is bounded?

Don't understand an induction solution.

Prove inequality with integer and real variables

Given $a_1=1, a_2=2, a_{n+1}=n(a_n+a_{n-1})$ find the general term

If $a$ can be written as sum of squares of three rational numbers, prove that $a^m$ can be too.

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