Verify: $ 1+2+3+\ldots+n=\frac{n(n+1)}{2} $, taking $ n=6 $ and $ 15 . $

Given :

\( 1+2+3+\ldots+n=\frac{n(n+1)}{2} \)

To do :

We have to verify the above equation by taking \( n=6 \) and \( 15 . \)

Solution :

Taking $n=6$,

LHS

$=1+2+3+4+5+6=21$

RHS

$=\frac{6(6+1)}{2}$

$=21$

LHS $=$ RHS

Taking $n=6$,

LHS

$=1+2+3+4+5+6+7+8+9+10+11+12+13+14+15=120$

RHS

$=\frac{15(15+1)}{2}$

$=\frac{15(16)}{2}$

$=120$

LHS $=$ RHS

Hence verified.

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Updated on: 10-Oct-2022

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