Question

Find the sum: $1+2+3+4+5+......+100$.

Answer 1

Calculate the sum of the given series:

Given series: $1,2,3,4,5,.....,100$.

The given series is in arithmetic progression.

The first term of the progression, $a=1$.

The last term of the progression, $l=100$.

The number of terms of the progression, $n=100$.

Thus, the sum of the given series can be given by, ${\mathit{S}}_{\mathit{n}}\mathbf{=}\frac{\mathit{n}}{\mathbf{2}}\mathbf{(}\mathbf{a}\mathbf{+}\mathbf{l}\mathbf{)}$.

$$\begin{gathered} \Rightarrow S_{100}=\frac{100}{2}\left(1+100\right) \\ \Rightarrow S_{100}=50\times 101 \\ \Rightarrow S_{100}=5050 \end{gathered}$$

Therefore, the sum $1+2+3+4+5+......+100=5050$.