Question

Sum of coefficients of the last $6$ terms in the expansion of ${(1+x)}^{11}$ when the expansion is in ascending powers of $x$, is

• A. $2048$
• B. $32$
• C. $512$
• D. $64$
• E. $1024$

Answer 1

The correct option is E $1024$

$(1+x{)}^{\prime \prime }={\sum }_{r=0}^{11}{n}_{C_r}(1{)}^{n-r}(x{)}^r$

$\text{last}6\text{terms of this expansion are}$

${}^{\prime \prime }{C}_{11}+{}^{\prime \prime }{C}_{10}+{}^{\prime \prime }{C}_q+{}^{\prime \prime }{C}_8+{}^{\prime \prime }{C}_7+{}^{\prime \prime }{C}_6$

$\text{using}{}^n{C}_r+{}^n{C}_{r+1}={}^{n+1}{C}_{r+1}$

$=12C_{11}+{}^{12}{C}_9+{}^{12}{C}_7$

$=12+220+792$

$=1024$