Q. 84.0( 3 Votes )
1.2 +2.22 + 3.22 +…. +n.2n = (n – 1) 2n+1 + 2.
P(1_ is trueAssuming P(k) is true.
1.2 +2.22 + 3.22 +…. +k.2k = (k – 1) 2 k+1 + 2
To prove P(k+1) is true using P(k) lies
1.2 +2.22 + 3.22 +…. +k.2k = (k + 1) 2 k+1 = (k)2 k+1+1 + 2
= k.2k+2 + 2 ……………(1)
L.H.S of (1)
1.2 + 2.22 + 3.22 +………..k.2k + (k+1)2(k+1)(k-1)2k+1 + 2 + (k +1) 2k+1
= 2k+1 (k+1+k-1)+2
= 2k+1 2k + 2
= 2k+2.k + 2
= k.2k+2 + 2
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
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Fundamental Principle of Counting49 mins
Game of Position & Momentum (Heisenberg Uncertainity principle)29 mins
Take the challenge, Quiz on Vectors37 mins
Vectors- Cosine & SIne Rule54 mins
Le Chatelier's Principle34 mins
Interactive Quiz on vector addition and multiplications38 mins
Addition of Vectors - Kick start Your Preparations47 mins
Scalar and Vector Product49 mins
Quiz on Heisenberg uncertainty principle35 mins
Scalar and vector product in one shot56 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
view all courses
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation