Answer :

To Prove:


, which is multiple of 7


Let us prove this question by principle of mathematical induction (PMI) for all natural numbers


is multiple of 7


Let P(n): , which is multiple of 7


For n = 1 P(n) is true since , which is multiple of 7


Assume P(k) is true for some positive integer k , ie,


= , where m N …(1)


We will now prove that P(k + 1) is true whenever P( k ) is true


Consider ,




[Adding and subtracting ]



[ Using 1 ]




, where r = is a natural number


Therefore is multiple of 7


Therefore, P (k + 1) is true whenever P(k) is true


By the principle of mathematical induction, P(n) is true for all natural numbers ie, 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
RELATED QUESTIONS :

Prove that cos α RD Sharma - Mathematics

Prove that sin x RD Sharma - Mathematics

Prove the followiRD Sharma - Mathematics

Prove the followiRD Sharma - Mathematics

Prove the followiRD Sharma - Mathematics

Prove the followiRD Sharma - Mathematics

Prove the followiRD Sharma - Mathematics

Prove the followiRD Sharma - Mathematics

Prove the followiRD Sharma - Mathematics

Prove that <span RD Sharma - Mathematics