Find the value of the following without addition:$1+3+5+7+9+11+13+15+17+19+21$

Given:

The given expression is $1+3+5+7+9+11+13+15+17+19+21$.

To do :

We have to find the sum of the given expression without adding.

Solution :

We know that,

The sum of 'n' consecutive odd numbers is $n^2$.

In the given sum there are 11 consecutive odd numbers.

Therefore,

$n =11$

$n^2 = 11^2 =121$.

Therefore, the value of $1+3+5+7+9+11+13+15+17+19+21$ is $121$.

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Updated on: 10-Oct-2022

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