Question

1+2+3+4+5....(n-1) + n = ?

Answer 1

n(n+1)/2

..,............

Answer 2

Looking at this series:

Let S = 1 + 2 + 3 + ...................... n - 1 + n

Now :

Last term is n

First term is 1.

If we add

==> n + 1

Second term + 3rd term is n - 1 + 2

==> n+ 1

So this gives n + 1 + n+ 1 + .................... n/2 times

Why n/2 times since :

two numbers are getting added to form 1 number

so n numbers form n/2 numbers

S = n + 1 + n + 1 .......................... n / 2 times

S = n / 2 ( n + 1 )

S = n ( n + 1 ) / 2

Thus the resultant sum is n ( n + 1 ) / 2

Hope it helps you

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