Question

proving that $\frac{d}{dx}\phi_j(x)=\frac{4}{l}\sum_{m=0 \\ (j+m) odd}^{j-1}\frac{3j-2m}{\xi_m}\phi_m(x)+\eta^l_j(x)$

score 90 · Answer 1 · 2019-08-14 02:25:28

90

Views

proving that $\frac{d}{dx}\phi_j(x)=\frac{4}{l}\sum_{m=0 \\ (j+m) odd}^{j-1}\frac{3j-2m}{\xi_m}\phi_m(x)+\eta^l_j(x)$

Published on 14 Aug 2019 - 2:25

score 94 · Answer 2 · 2019-08-14 03:15:36

94

Views

Proving inequalities with fractions: $(\frac{1}{2^n+1}+\frac{1}{2^n+2}+\frac{1}{2^n+3}+\ldots+\frac{1}{2^{n+1}})>\frac{1}{2}$

Published on 14 Aug 2019 - 3:15

score 29 · Answer 3 · 2019-08-14 07:40:59

29

Views

Series and Finitness -- Quotient of close terms bounded by close terms of finite series

Published on 14 Aug 2019 - 7:40

score 156 · Answer 4 · 2019-08-15 04:22:09

156

Views

Find the following finite sum

Published on 15 Aug 2019 - 4:22

score 68 · Answer 5 · 2026-03-26 17:53:22

68

Views

Show that the number of elements of $X$ belonging to a least $r$ equals to $\sum_{k=r}^n(-1)^{k-r}{k-1\choose r-1}S_k$

Published on 26 Mar 2026 - 17:53

score 99 · Answer 6 · 2026-03-25 07:46:09

99

Views

How to find $\sum_{r=1}^{n}\frac{1}{T_r}$ when $\sum_{r=1}^{n}T_r$ is given?

Published on 25 Mar 2026 - 7:46

score 59 · Answer 7 · 2019-08-17 02:24:22

59

Views

evaluating $\sum_{n=1}^{\infty}n\left(-\frac{1}{5}\right)^{n-1}$

Published on 17 Aug 2019 - 2:24

score 43 · Answer 8 · 2019-08-17 13:09:15

43

Views

Can the sum $\sum_{n=0}^{\infty} \frac{1}{a^{n(n+1)}}$ be explicitly evaluated?

Published on 17 Aug 2019 - 13:09

score 82 · Answer 9 · 2026-03-25 04:42:45

82

Views

Let $\alpha >0$ and $ \varepsilon > 0 $. Then $\sum_{n = 0}^{ + \infty} \frac{1}{(1 + |n^2 + n - \alpha |) (1 + n + n^2)^{\varepsilon}} < + \infty $?

Published on 25 Mar 2026 - 4:42

score 249 · Answer 10 · 2026-03-26 21:12:20

249

Views

Find sum $\sum _{k=0}^nF_kF_{n-k}$

Published on 26 Mar 2026 - 21:12

score 211 · Answer 11 · 2026-04-02 13:34:39

211

Views

Prove a combinatorial identity involving summing product of binomial coefficients

Published on 02 Apr 2026 - 13:34

score 66 · Answer 12 · 2019-08-19 00:23:00

66

Views

Find $\alpha$ ,with the given $\sum_{n=2}^\infty\left( \lim_{n \to \infty} \frac{g_n(f_n(a))}{a!} \right)=\alpha$

Published on 19 Aug 2019 - 0:23

score 94 · Answer 13 · 2019-08-19 03:38:07

94

Views

Find the sum of the series $1^3 + 3\cdot 2^2 + 3^3 + 3\cdot 4^2 + 5^3 + 3\cdot 6^2...$ up to $n$ terms

Published on 19 Aug 2019 - 3:38

score 124 · Answer 14 · 2026-04-04 16:54:22

124

Views

Show that $Q(Q(Q(2005^{2005})))=7$

Published on 04 Apr 2026 - 16:54

score 67 · Answer 15 · 2019-08-19 16:51:15

67

Views

A question related to limit and summation

Published on 19 Aug 2019 - 16:51

List Question

proving that $\frac{d}{dx}\phi_j(x)=\frac{4}{l}\sum_{m=0 \\ (j+m) odd}^{j-1}\frac{3j-2m}{\xi_m}\phi_m(x)+\eta^l_j(x)$

Proving inequalities with fractions: $(\frac{1}{2^n+1}+\frac{1}{2^n+2}+\frac{1}{2^n+3}+\ldots+\frac{1}{2^{n+1}})>\frac{1}{2}$

Series and Finitness -- Quotient of close terms bounded by close terms of finite series

Find the following finite sum

Show that the number of elements of $X$ belonging to a least $r$ equals to $\sum_{k=r}^n(-1)^{k-r}{k-1\choose r-1}S_k$

How to find $\sum_{r=1}^{n}\frac{1}{T_r}$ when $\sum_{r=1}^{n}T_r$ is given?

evaluating $\sum_{n=1}^{\infty}n\left(-\frac{1}{5}\right)^{n-1}$

Can the sum $\sum_{n=0}^{\infty} \frac{1}{a^{n(n+1)}}$ be explicitly evaluated?

Let $\alpha >0$ and $ \varepsilon > 0 $. Then $\sum_{n = 0}^{ + \infty} \frac{1}{(1 + |n^2 + n - \alpha |) (1 + n + n^2)^{\varepsilon}} < + \infty $?

Find sum $\sum _{k=0}^nF_kF_{n-k}$

Prove a combinatorial identity involving summing product of binomial coefficients

Find $\alpha$ ,with the given $\sum_{n=2}^\infty\left( \lim_{n \to \infty} \frac{g_n(f_n(a))}{a!} \right)=\alpha$

Find the sum of the series $1^3 + 3\cdot 2^2 + 3^3 + 3\cdot 4^2 + 5^3 + 3\cdot 6^2...$ up to $n$ terms

Show that $Q(Q(Q(2005^{2005})))=7$

A question related to limit and summation

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