Let n in N and [x] denote the greatest integer less than or equal to x. If the sum of (n + 1) terms ^nC_0,3.^nC_1,5.^nC_2,7.^nC_3,..... is equal to 2^(100) . 101, then 2[ n - 1 / 2 ] is equal to _______________.

Let nN and x denote the greatest integer less than or e... | (Mathematics)

${}^n{C_0} + 3.{}^n{C_1} + 5.{}^n{C_2} + ... + (2n + 1).{}^n{C_n}$ $\\{T_r} = (2r + 1){}^n{C_r}$ $\\S = \sum {{T_r}}$ $\\S = \sum {(2r + 1){}^n{C_r}} = \sum {2r{}^n{C_r} + \sum {{}^n{C_r}} }$ $\\S = 2(n{.2^{n - 1}}) + {2^n} = {2^n}(n + 1)$ $\\{2^n}(n + 1) = {2^{100}}.101 \Rightarrow n = 100$ $\\2\left[ {{{n - 1} \over 2}} \right] = 2\left[ {{{99} \over 2}} \right] = 98$

Explanation

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