Let the positive numbers a, b, c, d be in A. P. Then abc, abd, acd, bcd are
a, b, c, d are in A.P. Dividing each by abcd
also in A.P. Hence their reciprocals are in H.P.
Then x =
Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term is 3/4, then
Third term of a G.P > is 4. The product of first five terms is
The harmonic mean of the roots of the equation
The sum of the series 1/2 + 1/3 + 1/6 +……. to 9 terms is