a + ar + ar² +…..+ar^n-1 =

n (2) = a + ar = a(r+1)
R.H.S =
P(2) is true.
Let us assume p(k) is true lies
a + ar + ar² +…..+ar^k-1 =
To Prove p(k+1) is true using P(k)
a + ar + ar² +…..+ar^k-1+ar^k+1-1 = …………………(1)
L.H.S of (1)
a + ar + ar² +…..+ar^k-1+ar^k = a+r(a+ar+ar²+…ar^k-1)
                                       = a +
                                       =
                                       =
                                       =
                                       = =
Which is the R.H.S of (1)
P(K+1) is true.
By the Principle of mathematical induction, P(n) is true for all values of n where n N
Hence proved.