If the first and the nth term of aG.P are a and b, and P is the product of first n terms, prove :

Asked by  | 6th Jul, 2008, 11:35: PM

Expert Answer:

it is as we have inserted (n-2) G.M. between a and b.

r= (b/a)(n-2+1)= (b/a)(n-1)

so product of all these terms P= a.ar.ar2.ar3........ar(n-1)

 =an.r(1+2+3+.....(n-1))

=an.r(n*(n-1)/2)

put the value of r

P= an . (b/a)n/2 = (ab)n/2

i.e. P2=(ab)n.

Answered by  | 10th Aug, 2008, 05:16: PM

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