यदि `S=a+ar+ar^(2)+........... ar^(n-1)` तथा `r gt 1` तब `S=`........... .

a+ar+ar^(2)+......+ar^(n-1)=(a(r^(n)-1))/(r-1)

Show that the products of the corresponding terms of the sequences a, ar, ar^2 ,... ar^(n-1) and A, AR, AR^2 ,.... AR^(n-1) form a G.P, and find the common ratio.

If s=a+ar+ar^(2)+ar^(3)+.......oo then s_(oo)= . (|r|<1)

a+ar+ar^(2)+...+ar^(n-1)=(a(1-r^(n)))/(1-r) forall n in N.

Prove that a+ar+ar^2+.......+n "terms" =(a(r^n+1))/(r-1),r ne 1

If the sum of the first n terms of the series a + ar + ar^(2) +…+ ar^(n-1) +… oo is (a)/(1-r) , then -

Show that the products of the corresponding terms of the sequences a, ar,ar^(2),...,ar^(n-1) and A,AR,AR^(2),...,AR^(n-1) form a G.P,and find the common ratio.

Show that the products of the corresponding terms of the sequence a,ar, ar^(2),… ar^(n-1) and A,AR, AR^(2),…AR^(n-1) from a G.P. and find the common ratio.