Sum of series

how to find the sum of the series-
(1)x²+x⁴+x⁶+....+x²ⁿ
(2)1/x²+1/x⁴+....1/x²ⁿ.
Please tell in a proper stepwise manner.

1 Answers

106

Asish Mahapatra ·2009-04-08 02:41:56

(1) this is a GP with first term = x² and common ratio =x²
Applying the formula for sum of GP = a(rⁿ-1)/(r-1)
we have S = x²(x²ⁿ-1)/(x²-1)

(2) similarly for this one a=1/x² and r=1/x² and it is a GP
So, S = x^-2(x^-2n-1)/(x^-2-1)

√ √ || {} [] () → ~ ^ 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