Question

Coefficient of $x^n$ in the power series form of $\sqrt[3]{(1-2x)}$

score 1.3k · Answer 1 · 2017-03-09 01:25:48

1.3k

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Coefficient of $x^n$ in the power series form of $\sqrt[3]{(1-2x)}$

Published on 09 Mar 2017 - 1:25

score 4.5k · Answer 2 · 2017-03-09 20:22:24

4.5k

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Number of dissimilar terms in given expansion

Published on 09 Mar 2017 - 20:22

score 934 · Answer 3 · 2017-03-12 12:22:56

934

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Alternating sum of binomial coefficients identity

Published on 12 Mar 2017 - 12:22

score 69 · Answer 4 · 2017-03-15 01:51:47

69

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Binomial probability problem solving

Published on 15 Mar 2017 - 1:51

score 359 · Answer 5 · 2017-03-17 05:25:32

359

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Can Vieta's formulas be generalized?

Published on 17 Mar 2017 - 5:25

score 33 · Answer 6 · 2017-03-21 00:47:55

33

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Solve for $x$: $\sum_{r=0}^5 {5\choose r} (-1)^rx^{5-r}3^r = 32$

Published on 21 Mar 2017 - 0:47

score 209 · Answer 7 · 2026-03-25 20:53:31

209

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Is there a quick way of finding the coefficients in an expression like $(ax^3+bx^2+cx+d)^3$?

Published on 25 Mar 2026 - 20:53

score 151 · Answer 8 · 2017-03-23 22:54:36

151

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Show that $\lim_{n \rightarrow \infty} \frac{\Sigma_{i=0}^k \binom{n}{3i}}{2^n} = \frac{1}{3}$

Published on 23 Mar 2017 - 22:54

score 41 · Answer 9 · 2017-03-24 01:51:17

41

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Prove the Binomial Expansion with Induction

Published on 24 Mar 2017 - 1:51

score 1k · Answer 10 · 2026-03-30 14:59:08

1k

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Product of integral and fractional part of binomial expansion

Published on 30 Mar 2026 - 14:59

score 155 · Answer 11 · 2017-03-26 18:26:48

155

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If $c$ is equal to $\binom{99}{0}-\binom{99}{2}+\binom{99}{4}-\binom{99}{6}+\cdots+\binom{99}{96}-\binom{99}{98},$ then find $\log_2{(-c)}$.

Published on 26 Mar 2017 - 18:26

score 1.9k · Answer 12 · 2017-03-27 20:37:37

1.9k

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Solving binomial theorem via induction

Published on 27 Mar 2017 - 20:37

score 319 · Answer 13 · 2017-03-29 00:30:39

319

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Proving a Binomial Summation with Induction $\sum_{k=0}^n(-1)^k \binom nk^2$

Published on 29 Mar 2017 - 0:30

score 4.1k · Answer 14 · 2017-03-29 05:39:35

4.1k

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How to find the coefficient of $x^2y^3z^6$ in the expression $(x^2+y+z)^{10}$?

Published on 29 Mar 2017 - 5:39

score 78 · Answer 15 · 2017-03-29 19:15:22

78

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show that $\sum_{i=1}^{n} (-1)^{i+1}{{n}\choose{i}}\frac{1}{i(i+1)} = \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n+1}$

Published on 29 Mar 2017 - 19:15

List Question

Coefficient of $x^n$ in the power series form of $\sqrt[3]{(1-2x)}$

Number of dissimilar terms in given expansion

Alternating sum of binomial coefficients identity

Binomial probability problem solving

Can Vieta's formulas be generalized?

Solve for $x$: $\sum_{r=0}^5 {5\choose r} (-1)^rx^{5-r}3^r = 32$

Is there a quick way of finding the coefficients in an expression like $(ax^3+bx^2+cx+d)^3$?

Show that $\lim_{n \rightarrow \infty} \frac{\Sigma_{i=0}^k \binom{n}{3i}}{2^n} = \frac{1}{3}$

Prove the Binomial Expansion with Induction

Product of integral and fractional part of binomial expansion

If $c$ is equal to $\binom{99}{0}-\binom{99}{2}+\binom{99}{4}-\binom{99}{6}+\cdots+\binom{99}{96}-\binom{99}{98},$ then find $\log_2{(-c)}$.

Solving binomial theorem via induction

Proving a Binomial Summation with Induction $\sum_{k=0}^n(-1)^k \binom nk^2$

How to find the coefficient of $x^2y^3z^6$ in the expression $(x^2+y+z)^{10}$?

show that $\sum_{i=1}^{n} (-1)^{i+1}{{n}\choose{i}}\frac{1}{i(i+1)} = \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n+1}$

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