find coefficient

find coefficient of x⁴⁹ in expansion of (x+1)(x+2)(x+3)......(x+99)

2 Answers

Divide by x⁴⁹ to get

coefficient of 1 in
(1+1/x)(x+99) (1+2/x)(x+98) (1+3/x)(x+97) ............... (1+49/x)(x+51) (x+50)

(x+100+99/x) (x+100 + 2.98/x) (x+100+3.97/x) .... (x+100+49.51/x) (x+50)

Which is the same as 100⁴⁹.50 + coeff of 1/x in (x+100+99/x) (x+100 + 2.98/x) (x+100+3.97/x) .... (x+100+49.51/x)

which i can tthink of an easy way to figure out :(

What is the conclusion of the above solution?

√ √ || {} [] () → ~ ^ 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