Question

Find the sum of the first 10 natural numbers.

Answer 1

Let $S_{10}$ denote the sum to first 10 natural numbers.
$S_{10}=1+2+3+4+5+6+7+8+9+10$ ----(1)
Reversing the numbers and adding will not change the sum and hence,
$S_{10}=10+9+8+7+6+5+4+3+2+1$ ----(2)
Adding equation (1) & (2)
$2S_{10}=11+11+11+11+11+11+11+11+11+11$
$2S_{10}=11\times 10$
$\Rightarrow S_{10}=\frac{(11\times 10)}{2}=55$