- #1
ekko
- 6
- 0
hello, i am having some trouble with a few induction problems.
1) Prove by induction that for all natural numbers n, n^2 + 3 < 2^n + 5.
2) Prove by induction that for all natural numbers n, (1-1/2)(1-1/4)...(1-1/(2^n)) > or equal to 1/4 + 1/(2^(n+1)).
i got started on these but ran into dead-ends for both of them.
1) Prove by induction that for all natural numbers n, n^2 + 3 < 2^n + 5.
2) Prove by induction that for all natural numbers n, (1-1/2)(1-1/4)...(1-1/(2^n)) > or equal to 1/4 + 1/(2^(n+1)).
i got started on these but ran into dead-ends for both of them.