Question

The coefficient of $x$ in the expansion of $(14+x)(1+2x)(1+3x)....(1+100x)$ is

• A. 5050
• B. 10100
• C. 5151
• D. 4950

Answer 1

Answer: (A)

5050

Answer 2

The coefficient of $x$ in the expansion of
$(1+x)(1+2x)(1+3x)....(1+100x)$
$=1+2+3+....+100$
$=\frac{100(100+1)}{2}=50\times 101=5050$