Question

Without adding, find the sum: $1+3+5+7+9+11+13+15+17+19$

Answer 1

Find the sum $1+3+5+7+9+11+13+15+17+19$.

The sum of first $n$ odd natural numbers is $n^2$.

It can be observed that the given sum is sum of first $10$ odd natural numbers.

Thus,

$n=10$

So, the sum is,

$\begin{array}{rcl}1+3+5+7+9+11+13+15+17+19& =& {\left(10\right)}^2\\ & =& 10\times 10\\ & =& 100\end{array}$

Thus, the sum is $100$.