Question

Extending the same logic you’ve seen in the video so far, find out the sum of the first 10 natural numbers. (You can 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 us proceed as we have seen in the video to add 4 numbers.
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)
$2S_{10}=11+11+11+11+11+11+11+11+11+11$
$2S_{10}=11\times 10$
$\Rightarrow S_{10}=\frac{(11\times 10)}{2}=55$