Each of the following statements is an attempt to show that a given series is co

Question

Each of the following statements is an attempt to show that a given series is convergent or divergent. For each statement, enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter I.)

Use the limit comparison test with a p-series to determine whether the following series are convergent or divergent. Enter CONV for convergent, DIV for divergent , and the value of p.

Find dx / (9x-2)8 = (Enter its value if convergent and DIV if divergent) Use the integral test to determine whether 1/(9n-2)8 is convergent or divergent? Enter CONV if the series is convergent and DIV if divergent. Find 4dx / x2+1 = (Enter its value if convergent and DIV if divergent) Determine whether 4/n2+1 is convergent or divergent. Enter CONV if the series is convergent and DIV if divergent. For all n >2. 1/n ln(n), and the series 1/n diverges. So by the Comparison Test, the series 1/n ln(n) diverges. for all n > 3, 1/n2-7 1, n+1/n > 1/n, and the series 1/n diverges. So by the Comparison Test, the series n+1 / n diverges. Find the value of 4x2e-x3 dx = Determine whether 4n2e-x3 dx = Determine whether 4n2e-n3 is convergent or divergent Enter CONV if series is convergent, DIV if series is divergent. n3-1 / 7n10+1 is with p = n5/n6+3 is with p =

Explanation / Answer

A)(n^3-1)/(7n^10+1)=(1-1/n^3)/(7n^7+1/n^3)

(1-1/n^3)/(7n^7+1/n^3)<1/(7n^7+1/n^3)

1/(7n^7+1/n^3) converges so given limit converges

here p-series is 1/(7n^7+1/n^3)

B)n^5/(n^6+3) <1/(n^6+3)

and 1/(n^6+3) converges

So by comparision test given limit converges

Here p-series is 1/(n^6+3)

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