Question

find the value of 1+2+3+................. +50​

Answer 1

Solution:

We have to find the sum of the numbers from 1 to 50.

$\tt\longrightarrow S=1+2+3+4+...+50-(i)$

We can write the sum as:

$\tt\longrightarrow S=50+49+48+...+3+2+1-(ii)$

If we add both equations, we get:

$\tt\longrightarrow 2S=(1+50)+(2+49)+(3+49)+...+(50+1)$

$\tt\longrightarrow 2S=51+51+51+....+50\:times$

$\tt\longrightarrow 2S=51\times 50$

$\tt\longrightarrow S=\dfrac{2520}{2}$

$\tt\longrightarrow S=1275$

So, the sum of the numbers is 1275.

Alternative Way:

The formula to find sum of first n natural numbers is given by:

$\tt\longrightarrow S_{n}=\dfrac{n(n+1)}{2}$

Plugging n = 50, we get:

$\tt\longrightarrow S_{50}=\dfrac{50\cdot 51}{2}$

$\tt\longrightarrow S_{50}=1275$

Which is our required answer.