Question

pls answer this
1+2+3+4+5+......................+100

Answer 1

We have to find the sum of 1+2+3+4....upto...100.

1,2,3,4 .....100

We see these numbers are in AP having common difference of 1.

So we apply here the formula :-

Sⁿ = n/2 ( a + l )

Here a = 1.

l = 100

n = 100

Sⁿ = 100/2 ( 1 + 100 )

➡ 100/2 ( 101 )

➡ 50 × 101

➡ 5050.

Required answer is :-
Sum of 1+2+3+4......100 is 5050.

Hope it will help you !!!

Answer 2

1 + 2 + 3 + 4 + 5 + . . . . + 100 = 5050

Given :

The expression 1 + 2 + 3 + 4 + 5 + . . . . + 100

To find :

The value of the expression

Formula :

$\displaystyle \sf{1 + 2 + 3 + 4 + 5 + . . . . + n = \frac{n(n + 1)}{2} }$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

1 + 2 + 3 + 4 + 5 + . . . . + 100

Step 2 of 2 :

Find the value of the expression

We use the formula

$\boxed{ \: \displaystyle \sf{1 + 2 + 3 + 4 + 5 + . . . . + n = \frac{n(n + 1)}{2} } \: }$

Thus we get

$\displaystyle \sf{1 + 2 + 3 + 4 + 5 + . . . . + 100 }$

$\displaystyle \sf{ = \frac{100(100 + 1)}{2} }$

$\displaystyle \sf{ = \frac{100 \times 101}{2} }$

$\displaystyle \sf{ = 50 \times 101 }$

$\displaystyle \sf{ = 5050}$

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