The sum of coefficients of last 15 terms of the exapnsion $(1 + x)^{29}$ , when expanded in ascending powers of x is

2^{27}

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2^{28}

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2^{29}

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2^{30}

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Solution

The correct option is B $2^{28}$
Total number of terms = 30
sum of coefficients of last 15 terms, $S = 29 C 15 + 29 C 16 + 29 C 17 + 29 C 18 + . . . . . + 29 C 29 . . . . . (1)$

$Since, n C r = n C n - r S = 29 C 14 + 29 C 13 + 29 C 12 + . . . . . + 29 C 0 . . . . . . (2)$

adding (1) & (2) ,
$2 S = 29 C 0 + 29 C 1 + 29 C 2 + 29 C 3 . . . . . + 29 C 29 \Rightarrow 2 S = 2^{29} \Rightarrow S = 2^{28}$

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