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March 30, 2015

March 30, 2015

Posted by **Edwin** on Wednesday, September 23, 2009 at 3:28pm.

(c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also in A.P. (ii) a(b+c)/bc, b(a+c)/ca, c(a+b)/ab are also in A.P.

(d) if a^2, b^2, c^2 are in A.P, prove that (i) 1/(b+c), 1/(c+a), 1/(a+b) are also in A.P. (ii) a/(b+c), b/(c+a), c/(a+b) are also in A.P.

(e) the sum to infinity of a G.P series is R. The sum to infinity of the squares of the terms is 2R. The sum to infinity of the cubes of the terms is (64/13)R. Find (i) the value of R. (ii) the first term of the first original series.

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**MathMate**, Wednesday, September 23, 2009 at 6:13pm

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