Q7 of 104 Page 491

Prove that

It is Infinite Geometric Series.

Here,a = 1,

Formula used:Sum of an infinite Geometric series

∴ Sum = = R.H.S.

Hence, Proved that

If a, b, c are in GP and a^1/x = b^1/y = c^1/z then prove that x, y, z are in AP.

If a, b, c are in AP and x, y, z are in GP then prove that the value of x^{b - c}. y^{c - a}. z^{a - b} is 1.

Express as a rational number.