JEE Main & Advanced Mathematics Geometric Progression Special Series

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

 

\[={{1}^{3}}+{{2}^{3}}+{{3}^{3}}+{{4}^{3}}+.......+{{n}^{3}}=\sum\limits_{r=1}^{n}{{{r}^{3}}}={{\left[ \frac{n\,(n+1)}{2} \right]}^{2}}\].

 

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