doubt 2

what is the shortest method to find the values of -
(a)C_o/2-C₁/3+C₂/4-C₃/5...upto (n+1) terms.

(b)C₁/2+C₂/4+C₃/6+...

ans of (a) 1/(n+1)(n+2)

ans of (b) 2ⁿ-1/n+1

1 Answers

106

Asish Mahapatra ·2009-05-07 23:16:44

1. Consider the equation
(1-x)ⁿ⁺¹ = C₀ - C₁x + C₂x² - ...+C_n+1xⁿ⁺¹

multiply by x throughout and integrate wrt x and then put x=1

2. Consider: i am assuming to n terms
(1+x)ⁿ = C₀ + C₁x + C₂x²+ ...+C_nxⁿ
Divide both sides by x and then integrate. and then put x=1

U wud get the value for C1+C2/2+C3/3+...
multiply the value by 1/2 and u will get the answer

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