Special Series
Category : JEE Main & Advanced
(1) Sum of first n natural numbers
\[=1+2+3+.......+n=\sum\limits_{r=1}^{n}{r}=\frac{n\,(n+1)}{2}\].
(2) Sum of squares of first n natural numbers
\[={{1}^{2}}+{{2}^{2}}+{{3}^{2}}+.......+{{n}^{2}}=\sum\limits_{r=1}^{n}{{{r}^{2}}}=\frac{n\,(n+1)(2n+1)}{6}\].
(3) Sum of cubes of first n natural numbers
\[={{1}^{3}}+{{2}^{3}}+{{3}^{3}}+{{4}^{3}}+.......+{{n}^{3}}=\sum\limits_{r=1}^{n}{{{r}^{3}}}={{\left[ \frac{n\,(n+1)}{2} \right]}^{2}}\].
You need to login to perform this action.
You will be redirected in
3 sec
