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Mathematical induction on $ [R(\cos(t) + i\sin(t) )]^n = R^n(\cos(nt) + i\sin(nt)) $

score 1.1k · Answer 1 · 2026-04-15 00:15:09

1.1k

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Mathematical induction on $ [R(\cos(t) + i\sin(t) )]^n = R^n(\cos(nt) + i\sin(nt)) $

Published on 15 Apr 2026 - 0:15

score 30 · Answer 2 · 2026-04-16 20:40:38

30

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Need to use mathematical induction, I don't think I've proved it right though

Published on 16 Apr 2026 - 20:40

score 87 · Answer 3 · 2026-04-17 13:45:35

87

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Prove that $\sum_{k=1}^{n}(-1)^{k+1}\frac{1}{k}\binom{n}{k} = 1+\frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n}$

Published on 17 Apr 2026 - 13:45

score 161 · Answer 4 · 2026-04-15 21:24:44

161

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Given $f(n)=\sum_{k=0}^{n}2^k$, use mathematical induction to prove $f(n)=2^{n+1}-1$

Published on 15 Apr 2026 - 21:24

score 74 · Answer 5 · 2026-04-13 14:44:05

74

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Prove equivalence of two Fibonacci procedures by induction?

Published on 13 Apr 2026 - 14:44

score 45 · Answer 6 · 2026-04-14 02:06:56

45

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How to prove the relation between dimensions of linear subspaces and their vector space?

Published on 14 Apr 2026 - 2:06

score 121 · Answer 7 · 2026-04-16 12:11:51

121

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Find the flaw in the proof

Published on 16 Apr 2026 - 12:11

score 693 · Answer 8 · 2026-04-16 02:33:52

Prove by induction that, for all positive integers $n$ , if $\gcd(a,M_n)=1$ , then $a^{(p_1−1)(p_2−1)⋯(p_n−1)} \equiv 1 \pmod{M_n}$.

score 3k · Answer 9 · 2026-04-12 23:09:03

3k

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Maximum number of regions in which the plane can be split using $n$ lines.

Published on 12 Apr 2026 - 23:09

score 241 · Answer 10 · 2026-04-12 11:53:22

241

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What is wrong with this proof based on induction?

Published on 12 Apr 2026 - 11:53

score 74 · Answer 11 · 2026-04-15 06:24:06

74

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Can anyone help finish this proof? Induction proof $2^{n+2} \mid k^{2^n} -1$ for all $n \geq 1$ and odd $k$

Published on 15 Apr 2026 - 6:24

score 127 · Answer 12 · 2026-04-14 05:47:48

127

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Math Induction Series Proof

Published on 14 Apr 2026 - 5:47

score 106 · Answer 13 · 2026-04-15 16:21:46

106

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Prove by induction that Fn denotes the Fibonacci sequence $F_n=\sum_{j=0}^k {n-j \choose j} \text{ where k=}\left\lfloor\frac n2\right\rfloor$

Published on 15 Apr 2026 - 16:21

score 89 · Answer 14 · 2026-04-17 02:48:31

89

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Proving $\sum_\limits{k=0}^n \binom {k+m} {k} = \binom {m+n+1} {n}$ by induction.

Published on 17 Apr 2026 - 2:48

score 166 · Answer 15 · 2026-04-17 09:52:59

166

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$f-1$, $f$, $f+1$ cannot be all square

Published on 17 Apr 2026 - 9:52

List Question

Mathematical induction on $ [R(\cos(t) + i\sin(t) )]^n = R^n(\cos(nt) + i\sin(nt)) $

Need to use mathematical induction, I don't think I've proved it right though

Prove that $\sum_{k=1}^{n}(-1)^{k+1}\frac{1}{k}\binom{n}{k} = 1+\frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n}$

Given $f(n)=\sum_{k=0}^{n}2^k$, use mathematical induction to prove $f(n)=2^{n+1}-1$

Prove equivalence of two Fibonacci procedures by induction?

How to prove the relation between dimensions of linear subspaces and their vector space?

Find the flaw in the proof

Prove by induction that, for all positive integers $n$ , if $\gcd(a,M_n)=1$ , then $a^{(p_1−1)(p_2−1)⋯(p_n−1)} \equiv 1 \pmod{M_n}$.

Maximum number of regions in which the plane can be split using $n$ lines.

What is wrong with this proof based on induction?

Can anyone help finish this proof? Induction proof $2^{n+2} \mid k^{2^n} -1$ for all $n \geq 1$ and odd $k$

Math Induction Series Proof

Prove by induction that Fn denotes the Fibonacci sequence $F_n=\sum_{j=0}^k {n-j \choose j} \text{ where k=}\left\lfloor\frac n2\right\rfloor$

Proving $\sum_\limits{k=0}^n \binom {k+m} {k} = \binom {m+n+1} {n}$ by induction.

$f-1$, $f$, $f+1$ cannot be all square

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