Question

find the sum of first 100 natural numbers

Answer 1

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1 + 2 + 3 + 4 + … + 98 + 99 + 100

I noticed that if he was to split the numbers into two groups

Like (1 to 50 and 51 to 100)

I could add them together vertically to get a sum of 101.

1 + 2 + 3 + 4 + 5 + … + 48 + 49 + 50

100 + 99 + 98 + 97 + 96 + … + 53 + 52 + 51

1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
.
.
.
48 + 53 = 101
49 + 52 = 101
50 + 51 = 101

I realized then that his final total would be 50(101) = 5050.



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Answer 2

• The sum of first n natural no. = n(n+1)/2

                                                           =  100 x 101/2

                                                            =  50 x 101

                                                             = 5050

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