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The given series is diverges according to the P Test.
According to the statement
we have given that the a series and we have to find that the those series is a converges or diverges.
So, For this purpose, we know that the
P-series test to say whether or not the series converges.
So, The given series is
And then
The value of P becomes P = 5/6 < 1 when we find it using the p series test.
Hence, the p-series diverges
Because according to the p series test, The series converges if, and only if, the power satisfies p>1.
And diverges if, and only if, the power satisfies p<1.
So, The given series is diverges according to the P Test.
Learn more about Convergence and Divergence here
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Question:
Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 + 1/32 squareroot + 1/243 squareroot 3 + 1/1024 squareroot 4 + 1/3125 squareroot 5.
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