Binomial theorem

3.ⁿc₀-8.ⁿC₁+13.ⁿC₂-18.ⁿC₃.......... upto (n+1) terms =?

1 Answers

2305

Shaswata Roy ·2014-01-04 01:06:44

x^3(1-x^5)=x^3-\binom{n}{1}x^8+\binom{n}{2}x^{13}-\cdots

Differentiate and put x=1,

RHS is the required sum and LHS=

3x^2(1-x^5)^n-5n(x^7)(1-x^5)^{n-1}

If n=1 then the required sum is =-7 otherwise it is 0.

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