# Prove the following using the principle of mathematical induction for all n ∈ N1.2 + 2.22 + 3.23 + …+n.2n = (n – 1)2n + 1 + 2

Let the given statement be P(n), as Steps involved in solving a statement by mathematical Induction are:

Step 1: Verify that P(1) is true.
Step 2: If P(1) is true then P(2) is also true.

Step 1:

First, we check if it is true for n = 1, It is true for n = 1.

Now we assume that it is true for some positive integer k, such that …………..(1)

We shall prove that P(k + 1)is true,

Solving the left hand side with n = k + 1  [From equation (1)]    Which is equal to the Right hand side for n = k + 1.We proved that P(k + 1) is true.

Hence by principle of mathematical induction it is true for all n ∈ N.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Fundamental Principle of Counting49 mins  Prepare the Topic : Principle of Superpostion for Exams45 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  Quick Revision of Vector Addition and Multiplications37 mins
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 view all courses 