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Consider a G.P. with first term (1+x)^(n), |x| lt 1, common ratio (1+x)/(2) and number of terms (n+1). Let 'S' be sum of all the terms of the G.P., then sum_(r=0)^(n)"^(n+r)C_(r )((1)/(2))^(r ) equals |
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Answer» SOLUTION :`(C )` `sum_(r=0)^(n)'^(n+r)C_(r )((1)/(2))^(r )` `=^(n)C_(n)((1)/(2))^(0)+^(n+1)C_(n)((1)/(2))^(1)+^(n+2)C_(n)((1)/(2))^(2)+......+^(2n)C_(n)((1)/(2))^(n)` `="coefficient of"x^(n)"in" (1+x)^(n)((1)/(2))^(0)+(1+x)^(n+1)((1)/(2))^(1)+(1+x)^(n+2)((1)/(2))^(2)+....+(1+x)^(2n)((1)/(2))^(n)` `="coefficient of "x^(n)"in"S` `=2^(n)` |
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