Question

How do you find the sum of $1$ to $100$?

Answer 1

To find the sum of $1$ to $100$:

To find the sum of $n$ natural numbers, we can use the formula given below.

Sum of first $n$ natural numbers $=\frac{n(n+1)}{2}$

The sum of $1$ to $100$ means the sum of the first $100$ natural numbers.

Thus, substituting $n=100$ in the above formula,

The sum of $1$ to $100$ $=\frac{1}{2}100(100+1)$

$$\begin{gathered} =\frac{(100\times 101)}{2} \\ =50\times 101 \\ =5050 \end{gathered}$$

Hence, the sum of $1$ to $100$ is $\mathbf{5050}$.