Daily Practice Paper: 2009-09-22

2 Answers

Q2) 1.2+2.3+3.4+.....to n terms
T_n=n(n+1)
=n²+n
S_n=Î£T_n
=n(n+1)(n+2)/3

Ans1) Here the n^th term is
T_n = [1³+2³+3³+4³+5³+.........+n³ ] / [1+3+5+......+(2n-1)]

=
= (1/4) (n+1)²
= (1/4)n²+(1/2)n + (1/4)

Now sum of n terms ,

=(1/4) n (n+1)(2n+1) / 6 + (1/2) n(n+1) / 2 +(1/4)n

On solving we get,
S_n = (n/24) ( 2n²+9n+13)

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