Question

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

• A. $2^{27}$
• B. $2^{28}$
• C. $2^{29}$
• D. $2^{30}$

Answer 1

The correct option is B $2^{28}$

Total number of terms = 30
sum of coefficients of last 15 terms, $S=29C15+29C16+29C17+29C18+.....+29C29.....\left(1\right)$

$\mathrm{Since},nCr=nCn-rS=29C14+29C13+29C12+.....+29C0......\left(2\right)$

adding (1) & (2) ,
$2S=29C0+29C1+29C2+29C3.....+29C29\Rightarrow 2S=2^{29}\Rightarrow S=2^{28}$