Question

Find the sum of the first 10 natural numbers.
(Use $S_{10}=1+2+3+\dots +10$ and proceed)

• A. $10\times 11$
• B. $\frac{(10\times 11)}{2}$
• C. $\frac{(10\times 2)}{11}$
• D. None of these

Answer 1

The correct option is B

$\frac{(10\times 11)}{2}$

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)
$2S_{10}=11+11+11+11+11+11+11+11+11+11$
$2S_{10}=11\times 10$
$S_{10}=\frac{(11\times 10)}{2}=55$