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Proving that $\sum_{i=1}^n\frac{1}{i^2}<2-\frac1n$ for $n>1$ by induction

score 132 · Answer 1 · 2026-04-16 23:24:05

132

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Proving that $\sum_{i=1}^n\frac{1}{i^2}<2-\frac1n$ for $n>1$ by induction

Published on 16 Apr 2026 - 23:24

score 120 · Answer 2 · 2026-04-14 03:52:35

120

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Trouble with induction on polynomials

Published on 14 Apr 2026 - 3:52

score 79 · Answer 3 · 2026-04-17 05:41:15

79

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For $n \in Z^{\geq 0}$, define $g_n = 2^{2^n} + 1$. Show that $g_0\cdot g_1\cdots g_{n-1} = g_n -2$.

Published on 17 Apr 2026 - 5:41

score 351 · Answer 4 · 2026-04-17 01:17:25

351

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Proof that $3^c + 7^c - 2$ by induction

Published on 17 Apr 2026 - 1:17

score 749 · Answer 5 · 2026-04-16 12:09:59

749

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the sequence of Fibonacci numbers is defined as follows: $x_1=1, x_2=1$

Published on 16 Apr 2026 - 12:09

score 1.2k · Answer 6 · 2026-04-12 21:19:54

1.2k

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Prove by induction area of koch snowflake

Published on 12 Apr 2026 - 21:19

score 1.9k · Answer 7 · 2026-04-16 09:56:20

1.9k

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Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$

Published on 16 Apr 2026 - 9:56

score 338 · Answer 8 · 2026-04-16 01:12:40

338

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About the proof by induction that $\sum\limits_{i=1}^ni(i+1)=\frac13n(n+1)(n+2)$ for $n\geq 1$

Published on 16 Apr 2026 - 1:12

score 152 · Answer 9 · 2026-04-16 14:32:19

152

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Prove that $\gcd(g_a,g_b) = 1$ given that for $n \in Z^{\geq 0}$, define $g_n = 2^{2^n} + 1$

Published on 16 Apr 2026 - 14:32

score 1.9k · Answer 10 · 2026-04-16 10:58:49

1.9k

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CNF formula induction proof

Published on 16 Apr 2026 - 10:58

score 273 · Answer 11 · 2026-04-09 09:52:43

273

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Induction proof of sentence

Published on 09 Apr 2026 - 9:52

score 31 · Answer 12 · 2026-04-09 07:30:22

31

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A proof by strong induction for a recurrences defining function

Published on 09 Apr 2026 - 7:30

score 59 · Answer 13 · 2026-04-13 06:04:16

59

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Proof by Induction Using Fibonacci -- Not Sure About Other Question's Answers

Published on 13 Apr 2026 - 6:04

score 92 · Answer 14 · 2026-04-16 09:12:43

92

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Proving $2^{n+1} < n^2 + 2$ for $n\geq 0$ by induction

Published on 16 Apr 2026 - 9:12

score 64 · Answer 15 · 2026-04-10 00:20:52

64

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How to prove this equation I have come across by Induction?

Published on 10 Apr 2026 - 0:20

List Question

Proving that $\sum_{i=1}^n\frac{1}{i^2}<2-\frac1n$ for $n>1$ by induction

Trouble with induction on polynomials

For $n \in Z^{\geq 0}$, define $g_n = 2^{2^n} + 1$. Show that $g_0\cdot g_1\cdots g_{n-1} = g_n -2$.

Proof that $3^c + 7^c - 2$ by induction

the sequence of Fibonacci numbers is defined as follows: $x_1=1, x_2=1$

Prove by induction area of koch snowflake

Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$

About the proof by induction that $\sum\limits_{i=1}^ni(i+1)=\frac13n(n+1)(n+2)$ for $n\geq 1$

Prove that $\gcd(g_a,g_b) = 1$ given that for $n \in Z^{\geq 0}$, define $g_n = 2^{2^n} + 1$

CNF formula induction proof

Induction proof of sentence

A proof by strong induction for a recurrences defining function

Proof by Induction Using Fibonacci -- Not Sure About Other Question's Answers

Proving $2^{n+1} < n^2 + 2$ for $n\geq 0$ by induction

How to prove this equation I have come across by Induction?

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