a+ ar + ar2 + ...... + arn-1= a(rn-1)/r-1 prove this by PMI .
We need to prove that
using principle of Mathematical induction.
Let n = 1.
Plug-in this value in equation (1).
Thus, equation (1) is true for n = 1.
Let is true.
We need to prove that is true.
That is we need to prove that,
Consider the L.H.S of the above equation.
Since the statement is true for , we can rewrite :
Thus, if is true then is true.
Thus, is true for all .