A.P.

Find the sum of 2+5+10+17+26+.......to n terms.

2 Answers

106

Asish Mahapatra ·2010-06-07 00:26:39

S = 2 5 10 17 26 ...

A = 3 5 7 9 ....

T_A,n = 2n+1

T_S,n = T_S,1 + Î£T_A,n-1
= 2 + Î£(n=1 to n-1) (2n+1)
= 2 + (n-1)[6 + (n-2)*2]/2
= 2 + (n-1)(n+1)
= n² +1

=> Î£T_S,n (n=1 to n) = n(n+1)(2n+1)/6 + n

A (series) is the difference of the sum of the series of S (series)

T_A,n => nth term of the series A

S_n - S_n = 0

i.e. (2)+(5-2)+(10-5)+(17-10)+(26-17)+........-t_n=0

t_n=2+[3+5+7+9+.....to (n-1) terms
=2+n-12[2*3+(n-1-1)*2]
=2+(n-1)(2n-1)
=2n²-3n+3

So, S_n=Î£(2n²-3n+3)
=2*n(n+1)(2n+1)2-3*n(n+1)2+3*n
=n2(..............) <Express this in any form as you like in terms of 'n'>

Isn't this enough??

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