wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Prove the assertions of the following problems
Prove that 2n>n2 for any natural number n>5.

Open in App
Solution

n>5
(n1)2>2
n22n1>0
2n22n1>n2
2n2>n2+2n+1
2n2>(n+1)2
Let us assume 2n>n2
2n+1=2.2n>2n2>(n+1)2 which is true
By mathematical induction
2n>n2,when (n)>5

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Mathematical Induction
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon