Question

The $n^{th}$ term of series $\frac{1}{1}+\frac{1+2}{2}+\frac{1+2+3}{3}+....$ will be
[AMU 1982]

• A. $\frac{n+1}{2}$
• B. $\frac{n-1}{2}$
• C. $\frac{n^2+1}{2}$
• D. $\frac{n^2-1}{2}$

Answer 1

The correct option is A $\frac{n+1}{2}$

Given series $\frac{1}{1}+\frac{1+2}{2}+\frac{1+2+3}{3}+....$ So $n^{th}$ term of series is given by
$T_n=\frac{1+2+3+....+n}{n}=\frac{\frac{1}{2}n(n+1)}{n}=\frac{n+1}{2}$