IIT JEE , AIEEE Forum - Mathematics , Algebra

abhinav21

Find the sum of the series 1-2+3-4+5-6........to n terms.

Ksudha_iit

assume ...two series 1 3 5 .. and 2 4 6... consider two cases...when n is odd and n is even u ll get the sum

Ksudha_iit

or the difference is same - 1 .....whn n is even ..n odd two cases....

garima_1211

group as (1-2),(3-4),(4-5) & so on

No. of terms now is n/2

The common difference is -1

Thus the sum is n/4(-2) =-n/2

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nunoxic

Find the sum of the series 1-2+3-4+5-6........to n terms.

1+ 3 + 5 ............ - ( 2 + 4 + 6.........)

Consider Them Individually,

For The Summation 1 + 3 + 5 .......
Sn = n/2 (2 + (n-1)2)
= n / 2 ( 2 + 2n -2)
= n (n)
= n^2

For Summation 2 + 4 + 6...
Sn = n/2 (4 + ( n - 1)2)
= n/2(4 + 2n-2)
=n(1 + n)
=n^2 + n

Thus The Sum Of Overall Series Will Be

=n^2 - (n^2 + n)
= n^2 - n^2 - n
= -n

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