Question

Suppose that you have to calculate the sum S of all the numbers from 1 to 10:
S = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
Typically, we would add the numbers from left to right. However, there’s a more elegant way
to find S. Note that:
S = (1 + 10) + (2 + 9) + (3 + 8) + (4 + 7) + (5 + 6)
The sum of each pair above is 11, and hence S = 5 × 11 = 55.
Using a similar logic, find the sum S’ of all the numbers from 1 to 100:
S’ = 1 + 2 + 3 + … + 98 + 99 + 100

Answer 1

u can simply use the formula that is in AP

Answer 2

Given

S = 1 + 2 + 3 + .......+ 98 + 99 +100

S = (1+100) + (2+99) + (3+98) +......... + (98+3) +

(99+2) + (100+1)


◆◆◆The Sum of each pair above is 101

S ===> 50 × 101 ==> 5050