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Use the recursive definition of summation together with mathematical induction to prove a sequence

score 3.2k · Answer 1 · 2026-03-27 23:28:07

3.2k

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Use the recursive definition of summation together with mathematical induction to prove a sequence

Published on 27 Mar 2026 - 23:28

score 482 · Answer 2 · 2026-04-03 00:02:31

482

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Solving divide and conquer recurrence

Published on 03 Apr 2026 - 0:02

score 130 · Answer 3 · 2014-05-03 22:13:39

130

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Induction problem: a formula for $\sum_{i=1}^n i(i+1)$

Published on 03 May 2014 - 22:13

score 3.8k · Answer 4 · 2026-03-27 12:03:15

3.8k

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Use the principle of mathematical induction to show that the given statement is true for all natural numbers n.

Published on 27 Mar 2026 - 12:03

score 136 · Answer 5 · 2014-05-04 17:34:17

136

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Proof by induction that I'm stumped on.

Published on 04 May 2014 - 17:34

score 69 · Answer 6 · 2014-05-05 05:01:50

69

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Induction proof $a_n$ is even for n $\ge$ 1

Published on 05 May 2014 - 5:01

score 9.2k · Answer 7 · 2014-05-05 15:13:57

9.2k

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Is my induction proof of the handshake lemma correct? (Graph Theory)

Published on 05 May 2014 - 15:13

score 136 · Answer 8 · 2026-03-27 12:03:16

136

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Prove by mathematical induction for every natural number n. $5+25+125+\cdots+5^n=5/4(5^n-1)$

Published on 27 Mar 2026 - 12:03

score 23.4k · Answer 9 · 2026-03-27 04:23:51

23.4k

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Induction proof $F(n)^2 = F(n-1)F(n+1)+(-1)^{n-1}$ for n $\ge$ 2 where n is the Fibonacci sequence

Published on 27 Mar 2026 - 4:23

score 7.8k · Answer 10 · 2014-05-06 08:22:50

7.8k

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Proving that nth derivate of $x e^{-x}$ is $(-1)^n (e^{-x})(x-n)$ by induction.

Published on 06 May 2014 - 8:22

score 66 · Answer 11 · 2026-03-28 05:22:40

66

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List results of exponentiation, with natural bases and exponents

Published on 28 Mar 2026 - 5:22

score 57 · Answer 12 · 2014-05-06 17:41:17

57

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To prove $m$ is not a square of a natural number

Published on 06 May 2014 - 17:41

score 4.3k · Answer 13 · 2014-05-06 22:24:36

4.3k

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induction help proving the sum of the n powers of 2

Published on 06 May 2014 - 22:24

score 153 · Answer 14 · 2014-05-06 22:44:52

Prove that for every integer $n \ge 1$, $1 + \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+ ... +\frac{1}{\sqrt{n}}\le 2\sqrt{n}$

score 75 · Answer 15 · 2014-05-06 23:34:39

75

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Mix of contour integrals and mathematical induction?

Published on 06 May 2014 - 23:34

List Question

Use the recursive definition of summation together with mathematical induction to prove a sequence

Solving divide and conquer recurrence

Induction problem: a formula for $\sum_{i=1}^n i(i+1)$

Use the principle of mathematical induction to show that the given statement is true for all natural numbers n.

Proof by induction that I'm stumped on.

Induction proof $a_n$ is even for n $\ge$ 1

Is my induction proof of the handshake lemma correct? (Graph Theory)

Prove by mathematical induction for every natural number n. $5+25+125+\cdots+5^n=5/4(5^n-1)$

Induction proof $F(n)^2 = F(n-1)F(n+1)+(-1)^{n-1}$ for n $\ge$ 2 where n is the Fibonacci sequence

Proving that nth derivate of $x e^{-x}$ is $(-1)^n (e^{-x})(x-n)$ by induction.

List results of exponentiation, with natural bases and exponents

To prove $m$ is not a square of a natural number

induction help proving the sum of the n powers of 2

Prove that for every integer $n \ge 1$, $1 + \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+ ... +\frac{1}{\sqrt{n}}\le 2\sqrt{n}$

Mix of contour integrals and mathematical induction?

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