Q. 355.0( 1 Vote )

# Prove that  for all naturalnumbers, n ≥ 2.

Let P(n) = Let us find if it is true at n = 2,

P(2): P(2): Hence, P(2) holds.

Now let P(k) is true, and we have to prove that P(k + 1) is true.

Therefore, we need to prove that, P(k) = …….(1)

Taking L.H.S of P(k) we get,

P(k) = P(k + 1) = From equation (1),

P(k + 1) = P(k + 1) = P(k + 1) = P(k + 1) = Therefore, P(k + 1) holds.

Hence, P(n) is true for all n ≥ 2.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Take the challenge, Quiz on Vectors37 mins  Vectors- Cosine & SIne Rule54 mins  Addition of Vectors - Kick start Your Preparations47 mins  Scalar and Vector Product49 mins  Interactive Quiz on vector addition and multiplications38 mins  Revise Complete Vectors & it's application in 50 Minutes51 mins  Scalar and vector product in one shot56 mins  Quick Revision of Vector Addition and Multiplications37 mins  Quiz | Vector Addition and Multiplications35 mins  Unit Vectors24 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 