Maths Induction Question (1 Viewer)

[凍鴛鴦]

Hi again,

Can someone please help with this?

Prove by induction that:
(1+x)^n >= nx+1

n and x are positive integers

Thanks in advance!

 

[gman03]

Induction over n

true for n = 1

Assume true for n = k
that is, (1+x)^k >= kx+1


Then for n = k + 1

LHS = (1+x)^(k+1)
= (1+x) * (1+x)^k
>= (1+x) * (kx+1) (by induction)
= kx^2 + (k+1)x + 1
> 0 + (k+1)x + 1 (k is positive)
= (k+1)x + 1

So it is true for n = k + 1

Hence by induction the statement is true for positive n, x

 

[凍鴛鴦]

Cheers! Thanks heaps =D

 

[davidw89]

Induction over n

> 0 + (k+1)x + 1 (k is positive)
= (k+1)x + 1

Why did u replace x^2 with 0?

 

[Affinity]

Coz it suits him

 

[jyu]

Why did u replace x^2 with 0?

Because x^2 > 0 for positive x.