SOLUTION: Prove by induction that 3^n ≥ 2n +1 for all positive integers.

Question 909315: Prove by induction that 3^n ≥ 2n +1 for all positive integers.
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Prove .

n=1 case:
, yes.

ASSUME to be true. k is any natural number.

PROVE that k+1 case is true:

Divide both sides by 3

Compare this last found inequality with the ASSUMPTION statement inequality.
as you can compare in the corresponding positions in each statement.
The latter highlighted-in-green statement is also then true if the assumption
statement is true.
PROVED.

RELATED QUESTIONS
Prove by mathematical induction that: 2^2n - 1 is divisible by 3 for all positive... (answered by Edwin McCravy)

Pls help USE MATHEMATICAL INDUCTION TO PROVE THAT (n+1)^n < 2n^2 for all natural... (answered by ikleyn)

Prove by induction that for all positive integers value of n: {{{5^(2n)+3n-1}}} is an... (answered by Edwin McCravy)

use mathematical induction to prove that the statement is true for all positive integers. (answered by t0hierry,greenestamps)

Use mathematical induction to prove the statement is true for all positive integers n. (answered by Edwin McCravy)

Use mathematical induction to prove the statement is true for all positive integers n. (answered by ikleyn)

use mathematical induction to prove that 1^2 + 2^2 + 3^2 +...+ n^2 = n(n+1)(2n+1)/6... (answered by solver91311)

Use mathematical induction to prove the statement is true for all positive integers n. (answered by ikleyn)

Prove by mathematical induction that 3^(2n)-8n-1, n is a positive integer, is a multiple... (answered by Edwin McCravy)

SOLUTION: Prove by induction that 3^n &#8805; 2n +1 for all positive integers.

SOLUTION: Prove by induction that 3^n ≥ 2n +1 for all positive integers.