Question

The value of $\frac{1â‹\dots 2â‹\dots 3â‹\dots 4+2â‹\dots 3â‹\dots 4â‹\dots 5+3â‹\dots 4â‹\dots 5â‹\dots 6+……\text{ upto }16\text{ terms }}{1â‹\dots 2â‹\dots 3+2â‹\dots 3â‹\dots 4+3â‹\dots 4â‹\dots 5+……\text{ upto }16\text{ terms }}$ is equal to

• A. 16
• B. 400
• C. 64
• D. 80

Answer 1

Answer: (A)

$Θ\frac{1â‹\dots 2â‹\dots 3â‹\dots 4+2â‹\dots 3â‹\dots 4â‹\dots 5+3â‹\dots 4â‹\dots 5â‹\dots 6+…….\text{ upto }n\text{ terms }}{1â‹\dots 2â‹\dots 3+2â‹\dots 3â‹\dots 4+3â‹\dots 4â‹\dots 5+…...\text{ upto }n\text{ terms }}$
$=\frac{\frac{n(n+1)(n+2)(n+3)(n+4)}{5}}{\frac{n(n+1)(n+2)(n+3)}{4}}=\frac{4(n+4)}{5}$
For $n=16$, expression $=\frac{4×20}{5}=16$