How to solve 1+2+3+4+5 to 100

Welcome to my article How to solve 1+2+3+4+5 to 100. This question is taken from the simplification lesson.
The solution of this question has been explained in a very simple way by a well-known teacher by doing addition, subtraction, and fractions.
For complete information on how to solve this question How to solve 1+2+3+4+5 to 100, read and understand it carefully till the end.

Let us know how to solve this question How to solve 1+2+3+4+5 to 100.

First write the question on the page of the notebook.

How to solve 1+2+3+4+5 to 100

Let’s solve this question by writing it like this,

\displaystyle 1+2+3+4+5+\text{ }………..\text{+}100

This has been solved by arithmetic progression

where a= first term

n = no. of terms

d=common difference

Therefore

sum of n terms = Sn

and

a = 1

d = 1

n = 100

Formula

Sn = \displaystyle \frac{\mathbf{n}}{\mathbf{2}}\times \text{ }[\text{ }\mathbf{2}\text{ }\mathbf{a}+\left( {\mathbf{n}-\mathbf{1}} \right)\mathbf{d}]

Substituting the values of a , d , and n in this formula,

\displaystyle Sn=\frac{{100}}{2}\times \text{ }[\text{ 2}\times \text{ 1}+\left( {100-1} \right)1]

\displaystyle Sn=50\times \text{ }[\text{ 2}+\left( {99} \right)1]

\displaystyle Sn=50\times \text{ }[\text{ 2}+99]

\displaystyle Sn=50\times \text{ }[\text{ 101}]

\displaystyle Sn=50\times 101

\displaystyle Sn=5050 [Answer]

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