Question

find the value 1,2 3 ........100​

Answer 1

The complete question is as follows.

Find the value of the sum of $1, 2, 3,......, 100$

Final Answer:

The calculated value of the sum of $1, 2, 3,......, 100$ is $5050$.

Given:

The series of the first hundred natural numbers  $1, 2, 3,......, 100$

To Find:

The sum of the numbers  $1, 2, 3,......, 100$ is to be found out.

Explanation:

The natural numbers are al the positive numbers that ranges from the value $1$ to infinity.

Note that the following is the formula for calculating the sum of the first "n" natural numbers.

$S_{n} = 1+2+3+4+....+n\\=\frac{n*(n+1)}{2}$

Step 1 of 3

Since, the sum of the natural numbers starting from the first one up to the hundredth one is to be found out, put $n=100$ in the above formula

Step 2 of 3

On putting $n=100$, this calculation follows.

$S_{n=100} \\= 1+2+3+4+....+100\\=\frac{100*(100+1)}{2}$

Step 3 of 3

Simplify the above numerical expression in the following way.

$\frac{100*(100+1)}{2}\\=\frac{100*101}{2}\\=50*101\\=5050$

Therefore, the required value of the sum of $1, 2, 3,......, 100$ is $5050$ which is the correct answer.

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