Question

Find the ${20}^{th}$ term in the binomial expansion of $(1+x{)}^{20}$ when $x=-5$

• A. $-20\times 5^{19}$
• B. $20\times 5^{20}$
• C. $-20\times 5^{20}$
• D. $20\times 5^{19}$

Answer 1

The correct option is A

$-20\times 5^{19}$

We want to find the ${20}^{th}$ term or $T_{20}$
We know $T_{r+1}={}^n{C}_r{x}^{n-r}{y}^r$ in the expansion of $(x+y{)}^n$
$T_{r+1}$ in the expansion of $(1-x{)}^{n}is{}^n{C}_r{(-x)}^r$
$\Rightarrow T_{20}=(-1{)}^{19}\cdot {}^{20}{C}_{19}\cdot x^{19}$ (Because r=19 in this case)
=$-20\times 5^{19}$