SOLUTION: For what values of n does {{{(2x^3-1/x)^n}}}, have a non-zero constant term?

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Question 1153471: For what values of n does %282x%5E3-1%2Fx%29%5En, have a non-zero constant term?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are n factors of (2x^3-1/x).

To get a constant partial product, you need to pick the "-1/x" term 3 times as often as you pick the "2x^3" term.

That means the number of factors must be a multiple of 4.

ANSWER: The exponent n can be any positive multiple of 4.

Example 1: n=4

The next-to-last term in the expansion is



Example 2: n=8

The second from last term in the expansion is