binomial

for |x| < 1
1 + 3x + 6x² + 10x³............. = ?

4 Answers

The rth term is given by \frac{r(r+1)}{2}x^r-1

Now you want to find the sum

You can think of this as the derivative of something?

And then take the sum (Infact the double derivative?)

Give it a shot once...

Err , I think that -

Now , from the fundamentals of infinite G . P . - s ,

Differentiate each side of this identity twice to get -

262

Aditya Bhutra ·2011-06-18 11:18:10

from, binomial expansion for any index, we have
(1+x)^-3 = 1-3x + 6x² - 10x³ ......
now replacing x with -x,

(1-x)^-3 = 1+3x + 6x² + 10x³ ......

thanks for all your help..
i got another method too..using agp

√ √ || {} [] () → ~ ^ 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