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To test the series ?_{k=1}^? 1/?(k²) for convergence, you can use the P-test. (You could also use the Integral Test, as is the case with all series of this type.) According to the P-test: the P-test does not apply to ?_{k=1}^? 1/?(k²) ?_{k=1}^? 1/?(k²) diverges ?_{k=1}^? 1/?(k²) converges Now compute s?, the partial sum consisting of the first 5 terms of ?_{k=1}^? 1/?(k²): s? =

          To test the series ?_{k=1}^? 1/?(k²) for convergence, you can use the P-test. (You could also use the Integral Test, as is the case with all series of this type.) According to the P-test:

the P-test does not apply to ?_{k=1}^? 1/?(k²)
?_{k=1}^? 1/?(k²) diverges
?_{k=1}^? 1/?(k²) converges

Now compute s?, the partial sum consisting of the first 5 terms of ?_{k=1}^? 1/?(k²):

s? =

Show more…

To test the series ?k=1^? 1/?(k²) for convergence, you can use the P-test. (You could also use the Integral Test, as is the case with all series of this type.) According to the P-test:

the P-test does not apply to ?k=1^? 1/?(k²)
?k=1^? 1/?(k²) diverges
?k=1^? 1/?(k²) converges

Now compute s?, the partial sum consisting of the first 5 terms of ?k=1^? 1/?(k²):

s? =

Added by F-Tima S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Manisha Sarker

08/23/2023

Step 1

Since it is not provided, let's assume it is a general p-series: $$\sum_{n=1}^{\infty} \frac{1}{n^p}$$ Now, we can apply the P-test. The P-test states that if $p > 1$, the series converges, and if $p \leq 1$, the series diverges. Now, let's compute the partial Show more…

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To test the series for convergence, you can use the P-test. (You could also use the Integral Test, as is the case with all series of this type.) According to the P-test, Now compute s5, the partial sum consisting of the first 5 terms.

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