Question

prove using induction

Answer 1

for \[h>-1\]
\[1+nh \leq (1+h)^n\] for all non-negetive intergers n

Answer 2

base case
\[1+n(0) \leq (1+0)^n,1 \leq 1\]

Answer 3

"Bernoullis inequality"

Answer 4

let n=1
1+h<=1+h
which is true
let n=N is also true i.e.
1+Nh<=(1+h)^N----------------------(a)
now for n=N+1
1+(N+1)h
=1+Nh+1
using (a)
2+Nh<=[(1+h)^N]+1<=(1+h)^(N+1)
:)

Answer 5

@Jonask