Binomial Theorem

Find the coefficient of x^r in the following-

(x+2)ⁿ+(x+2)^n-1(x+1)+(x+2)^n-2(x+2)²+.....+(x+1)ⁿ

2 Answers

1133

Sourish Ghosh ·2014-01-03 22:40:02

ⁿ⁺¹C_r(2^n+1-r -1)

2305

Shaswata Roy ·2014-01-04 00:44:47

(x+2)^n+(x+2)^{n-1}(x+1)+\cdots +(x+1)^n
\frac{(x+2)^{n+1}-(x+1)^{n+1}}{(x+2)-(x+1)}=(x+2)^{n+1}-(x+1)^{n+1}

â†’Coefficient of x^r=ⁿ⁺¹C_r(2^n+1-r-1)

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

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° ∂ ∞ 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