Question

Prove by induction that
4n!>2^(n+2) for all n>=4

Answer 1

what is >=

Answer 2

=>

Answer 3

greater equal to

Answer 4

Greater of equal obviously

Answer 5

alright

Answer 6

i am trying to prove that
\[4(n+1)!>2^{(n+1)+2}\]

Answer 7

Proofs by induction are simple. You check it is true for the base case, which is 4, assume it is true for n and prove that it is true for n+1

Answer 8

\[4(n+1)!=4(n+1)n!>2^{n+3}\]

Answer 9

\[=>4n!(n+1)>2^{n+2}(n+1)\]

Answer 10

Never mind, i read this wrong, it is difficult to figure out these drawings.

Answer 11

Actually looking over this, your proof is a fallacy

Answer 12

It means that you have started the whole proof resting on the case that the proof holds.

Answer 13

The very first thing you have stated is 4(k+1)!>2^(k+1)+2 which is what you are trying to prove

Answer 14

A fallacy is a falsehood.
Something inaccurate. Lulz.

Answer 15

Again you started your proof with the assumption that 4(k+1)!>=2^(k+2)+1 holds

Answer 16

which is what you need to prove.