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7. Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that \(P^2 R^n=S^n\).

8. If a,b,c,d are in G.P, prove that \((a^n+b^n )\),\((b^n+c^n )\),\((c^n+d^n)\) are in G.P.

11. Find the sum of the following series up to n terms:

(i) 5+55+555+ …….…

(ii) .6+.66+.666+…………..

12. Find the 20th term of the series 2×4 + 4×6 + 6×8 + … + n terms.