Question

What is the total number of words of length $500$ on $\{a,b\}$ such that the letter $"a"$ appears more than $"b"$ ( without Brute force)?

score 64 · Answer 1 · 2026-03-26 22:55:20

64

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What is the total number of words of length $500$ on $\{a,b\}$ such that the letter $"a"$ appears more than $"b"$ ( without Brute force)?

Published on 26 Mar 2026 - 22:55

score 45 · Answer 2 · 2024-03-03 10:40:17

45

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Find $n$ when the coefficients of the $16^{th}$ and $26^{th}$ terms of $(1+x)^n$ are equal.

Published on 03 Mar 2024 - 10:40

score 127 · Answer 3 · 2024-03-06 23:02:20

127

Views

Proof $\displaystyle \sum_{k=0}^n \binom{2n}{2k} = 2^{2n-1}$

Published on 06 Mar 2024 - 23:02

score 35 · Answer 4 · 2024-03-08 07:14:05

35

Views

Arithmetic sequence in coefficients of $(x+y)^n$

Published on 08 Mar 2024 - 7:14

score 18 · Answer 5 · 2026-03-30 12:04:17

18

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Cumulative Distribution Function (CDF) of a Binomial Distribution

Published on 30 Mar 2026 - 12:04

score 38 · Answer 6 · 2024-03-08 17:40:12

38

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Binomial Theorem Coefficients derivation

Published on 08 Mar 2024 - 17:40

score 64 · Answer 7 · 2024-03-15 15:02:00

64

Views

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

Published on 15 Mar 2024 - 15:02

score 73 · Answer 8 · 2024-03-18 09:59:20

73

Views

An application of binomial theorem

Published on 18 Mar 2024 - 9:59

score 26 · Answer 9 · 2024-03-19 20:44:49

26

Views

A property of product of sequence being small

Published on 19 Mar 2024 - 20:44

score 44 · Answer 10 · 2024-03-20 19:19:55

44

Views

$ \sum_{k=0}^{n}\mathrm{C}_{2k}^{n+k} {(-4)}^{k} $

Published on 20 Mar 2024 - 19:19

score 52 · Answer 11 · 2024-03-23 22:03:21

52

Views

How to Prove the Binomial Series by Differentiation?

Published on 23 Mar 2024 - 22:03

score 34 · Answer 12 · 2024-03-24 21:51:34

34

Views

AB is a chord of length 2ka of a circle of radius a. The tangents to the circle at A and B meet in C if k^7 is negligible calculate the area of ABC

Published on 24 Mar 2024 - 21:51

score 54 · Answer 13 · 2024-03-26 15:51:24

54

Views

Can we use Binomial Approximations when evaluating limits?

Published on 26 Mar 2024 - 15:51

score 109 · Answer 14 · 2015-01-05 19:13:10

109

Views

Why does $\sum_{k=1}^{n-1}{n \choose k} = -1 -1 + \sum_{k=0}^{n} {n \choose k}$ by the binomial theorem?

Published on 05 Jan 2015 - 19:13

score 37 · Answer 15 · 2015-01-05 22:01:21

37

Views

Integer sum of powers

Published on 05 Jan 2015 - 22:01

List Question

What is the total number of words of length $500$ on $\{a,b\}$ such that the letter $"a"$ appears more than $"b"$ ( without Brute force)?

Find $n$ when the coefficients of the $16^{th}$ and $26^{th}$ terms of $(1+x)^n$ are equal.

Proof $\displaystyle \sum_{k=0}^n \binom{2n}{2k} = 2^{2n-1}$

Arithmetic sequence in coefficients of $(x+y)^n$

Cumulative Distribution Function (CDF) of a Binomial Distribution

Binomial Theorem Coefficients derivation

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

An application of binomial theorem

A property of product of sequence being small

$ \sum_{k=0}^{n}\mathrm{C}_{2k}^{n+k} {(-4)}^{k} $

How to Prove the Binomial Series by Differentiation?

AB is a chord of length 2ka of a circle of radius a. The tangents to the circle at A and B meet in C if k^7 is negligible calculate the area of ABC

Can we use Binomial Approximations when evaluating limits?

Why does $\sum_{k=1}^{n-1}{n \choose k} = -1 -1 + \sum_{k=0}^{n} {n \choose k}$ by the binomial theorem?

Integer sum of powers

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