Finding Values In Exercises 45-50 Find the positive values of p for which the series converges.
To calculate: The positive values of p are for which the given series would converge.
The series, .
Integration of .
Integration by parts ,
Take the priority of the function from ILATE method.
I for inverse function, L for logarithmic function, A for algebraic function, T for trigonometric function and E for exponential function.
Here, is continuous and decreasing for . So, f satisfies the conditions required for the integral test.
Now, use integration by parts,
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