Question

Solve the given expression:

$n[1+\frac{1}{n}][1+\frac{1}{n+1}]....[1+\frac{1}{n+m}]$

• A. $n+m$
• B. $n+m+1$
• C. $m$
• D. $m-n+1$

Answer 1

Answer: (B)

$n+m+1$

Taking first $2$ brackets

$n[1+\frac{1}{n}]=n\left[\frac{n+1}{n}\right]=n+1$

Now,

$(n+1)[1+\frac{1}{n+1}]=(n+1)\left[\frac{n+2}{n+1}\right]=n+2$

Similarly, next two brackets will give final term as $n+3$ and so on..

With this pattern, we can see that, answer will be the numerator of the last term

i.e. Numerator of $[1+\frac{1}{n+m}]=n+m+1$