try it

$S_k = \mathop{\lim}\limits_{n \to \infty} \sum_{i=0}^{n}\frac{1}{( k+ 1)^i}$

find

$\sum_{k=1}^{n} kS_k$

(prctc)

$\sum_{n=1}^{m} n.n!$

7 Answers

second is easy write n.n! = (n+1 - 1 ).n! = (n+1) ! - n !

in first one
Sk is a gp na ??

yup

Q-1

-n ??

tip : before giving infinite series please also give the convergence conditions

1- no.

( convergence / divergence not needed here and also not mentioned in the question.& i think qwerty bhai's # 3 is enough as a hint)

ya made a mistake

\sum{k+1}=\frac{n(n+1)}{2}+n = \frac{n(n+3)}{2}

yes .. crct answer

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω