Find the value of

VITEEE 2015 Sample Questions › Algebra questions › Find the value of

C₀/2+2C₁/3+3C₂/4+...+(n+1)C_n/(n+2)

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Ketan Chandak ·2013-01-16 06:03:20

rearranging the given expression,
C₀-C₀/2+C₁-C₁/3....

which is (C₀+C₁+C₂....)-(C₀/2+C₁/3+C₂/4...)

the first bracket series upto n terms is 2ⁿ and the second bracket sum can also be found out by writing the binomial expansion of x(1+x)ⁿ,integrating it and putting x=1.

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Jeet Sen Sharma ·2013-01-31 04:01:50

it can easily be done. multipling both sides by x thn integrating, thn dividing both sides by x thn differentiating and putting x=1 in the expansion of (1+x)ⁿ.

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Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ 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

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