Prove the following by using the principle of mathematical induction for all
(2n+7) < (n+ 3)2
can any pls explain this question in detail??? cuz i can't get it
Arjun listen
Assuming that you know how to prove P(1) is true, let us start with p(k)
(2k+7)<(k+3)^2 (Add 2 on both sides) (Because we have to prove that p(k+1) is also true)
2k+7+2 < k^2 + 6k + 9 +2
2k+9 < k2 + 6k + 11 ------------- (4)
Know in rough subsitute the valu of p(n)= k+1
you will get = k2 + 8k + 16 in RHS
And LHS would be 2k + 9
we know 8k > 6k ------(1)
16 > 11 -------(2)
Add (1) and (2)
8k + 16 > 6k + 11
Add k2 on both sides
k2 + 8k + 16 > k2 + 6k + 11 --------------(3)
From (3) and (4)
2k + 9 > k2 + 8k + 16
Which is equal to P(k + 1).................
Therefore it is true for all n E N
Hope i'm clear !!!!!!!!!!!! Thumps up please