Q. 1

1+3+3<sup

Answer :


Let P(n) = 1+3+32 +… +3n-1
P(1) is true
Assuming P(k) is true
1+3+32 +… +3k-1 =
To prove P(k +1) is true using the result of P(k)
1+3+32 +… +3k-1 +3k = ……………(1)
proof: Taking L.H.S of (1)
1+3+32 +… +3k-1 +3k
                               = + 3k
                               = =
                               =

Which is the R.H.S of (1)

P(K + 1 ) is true

By the Principle of Mathematical induction, given expression is true for all values of n .
When n N
Hence proved.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses