Prove that 1 + 3n≤ 4n, for every integern≥ 0.

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- Mar 13th 2010, 07:13 PMbearej50Mathematical InductionProve that 1 + 3
*n*≤ 4*n*, for every integer*n*≥ 0.

- Mar 13th 2010, 07:23 PMJhevon
Where did you get stuck? This one was not

*that*difficult. I'll just give the solution. It doesn't work for zero, you can check this.

Define a statement by for all integers

We show that is true using mathematical induction.

Since , we have that is true.

Assume that is true, we show that holds also.

Note that,

So that , which is . Thus, holds by induction.