# math

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(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number.

(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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