Question

1. To test the series ∞∑k=1 1/5√k^3 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:

• ∞∑k=1 1/5√k^3 converges
• the P-test does not apply to ∞∑k=1 1/5√k^3
• ∞∑k=1 1/5√k^3 diverges

Now compute s4, the partial sum consisting of the first 4 terms of ∞∑k=1 1 /5√k^3:

s4=

2. Test the series below for convergence using the Ratio Test.
∞∑n=1 n^5 /1.2^n
The limit of the ratio test simplifies to lim n→∞ |f(n)| where
f(n)=   
The limit is:    
Based on this, the series diverges or converges?

Answer 1