8.The sum of the series1-3+5-7+9-11+..to n terms isA)-n, when n is eve

1.	8.The sum of the series1-3+5-7+9-11+..to n terms isA)-n, when n is even B) n, when n is evenC)-n, when n is oddD) none of these
Answer» 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)

8.The sum of the series1-3+5-7+9-11+..to n terms isA)-n, when n is even B) n, when n is evenC)-n, when n is oddD) none of these

Answer»

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)