Q. 175.0( 3 Votes )
Prove the following by the principle of mathematical induction:
a + ar + ar2 + … + arn – 1
Answer :
Let P(n): a + ar + ar2 + … + arn - 1 = 
For n =1
a = a
a = a
Since, P(n) is true for n = 1
Let P(n) is true for n = k , so
P(k): a + ar + ar2 + … + ark - 1 = 
- - - - - - - (1)
We have to show that,
a + ar + ar2 + … + ark - 1 + ark = 
Now,
{ a + ar + ar2 + … + ark - 1} + ark
= 
using equation (1)
= 
= 
= 
Therefore, P(n) is true for n = k + 1
Hence, P(n) is true for all n ∈ N
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