Question

The sum of series $1.2+2.3+3.4+....10$ terms is

• A. $440$
• B. $286$
• C. $524$
• D. $\infty$

Answer 1

Answer: (A)

$440$

$1.2+2.3+\mathrm{3.4........10}$terms

The general terms of the above series can be written as

$T_n=n(n+1)$

$\therefore S_n=$Sum of $n$ terms of the series.

$=\sum T_n=\sum n(n+1)=\sum (n^2+n)=\sum n^2+\sum n=\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}=\frac{n(n+1)}{2}[\frac{2n+1}{3}+1]=\frac{n(n+1)(n+2)}{3}\therefore S_{10}=\frac{10\times 11\times 12}{3}=10\times 44=440$