Determine for which positive integer values of n, 3n^3+2≤n^4 and prove your claim by mathematical induction. I was able to determine n must be greater or equal to 4. But I can't seem to get through the inductive step.
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Find the critical number(s)
Therefore for .
Let be the proposition that
is true, because
We assume that Under this assumption, it must be shown that is true, namely, that
Hence is true under the assumption that is true. This completes the inductive step.
We have completed the basis step and the inductive step, so by mathematical induction we know that is true for integers . That is, we have proven that