21: There is just one trouble, at infinity. The integral can be evaluated, but seventy integrations by parts do not seem like a good idea. The Limit Comparison test is also out, since there are no unimportant (at infinity) parts added. The only hope is from the Comparison test, trying to find a convergent upper bound.

Recall that x⁷⁰ ≤ e ^x for large values of x, but check that this would lead to a test function with divergent integral, allowing for no conclusion.

The trick here is to use a better inequality, where we take a "smaller exponential". Indeed, using a limit argument one can prove that x⁷⁰ ≤ e ^x/2 for large values of x. Use this to set up the Comparison test.

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