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Find the sum of the series- 1 – 3 + 5 – 7 + 9 – 11 + ……upto n terms.

Find the sum of the series-
1 – 3 + 5 – 7 + 9 – 11 + ……upto n terms.

Grade:11

1 Answers

GAURAV AGRAWAL
29 Points
8 years ago

1-3+5-7+9-11+....................upto n terms,

1+5+9+................till n/2 terms

 =n/4(2n-2)

 =n(n-1)/2-----------------------------------------1

3+7+11+15+......................till n/2 terms

=n/4(2n+4)

=n(n+2)/2----------------------------------------2

so,1-3+5-7+9-.................................n terms

=n(n-1)/2-n(n+1)/2-------------------------------------from 1 and 2

=n/2(n-1-n-2)

=-3n/2

so,answer is(-3n/2)

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