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

Prove that : (2n+7)<(n+3)2

Open in App
Solution

Let's,

P(n) = (2n+7)<(n+3)2

【For n = 1】

So,

L.H.S,

2n+7

= (2 × 1) + 7

=9

R.H.S,

(n+3)3

=(1+3)3

=(4)3

=16

[Note:- the value of 'n' can be anything]

Hence, We Can Say, (2n+7)<(n+3)3
Another Process

Let's, P(k) is True.

(2k+7)<(n+3)2 .......(i)


L.H.S = (2(k+1)+7)

R.H.S = ((k+1)+3)2

L.H.S

(2(k+1)+7)

=2k+2+7

=(2k+7)+2

[Using (i)]

<(k+3)2+2

<k2+2.k.3+(3)2+2

<k2+6k+9+2

<k2+6k+11

R.H.S

((k+1)+3)2

=(k+4)2

=k2+2.k.4+(4)2

=k2+8k+16

Now, Compare Both Sides,

6k < 8k

11 < 16

So We Can Say,

(2n+7)<(n+3)2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Introduction to Algebraic Expressions and Identities
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon