Series: Comparison Tests    Lecture Video

1. Use ''The (Direct) Comparison Test'' to determine if each of  the following series is convergent or divergent.

(a) \(\displaystyle{\sum_{n=1}^{\infty}\frac{1}{n^2+3n+5}}\)   solution

(c) \(\displaystyle{\sum_{n=1}^{\infty}\frac{2^n}{3^n+1}}\)   solution

(b) \(\displaystyle{\sum_{n=1}^{\infty}\frac{n^2}{n^3-2}}\)   solution

(d) \(\displaystyle{\sum_{n=1}^{\infty}\frac{\cos^2 n}{n^3}}\)   solution

Use ''The Limit Comparison Test'' to determine if each of  the following series is convergent or divergent.

(a) \(\displaystyle{\sum_{n=1}^{\infty} \frac{1}{3n+5}}\)   solution

(b) \(\displaystyle{\sum_{n=1}^{\infty} \frac{5n^4+2\cdot3^n-1}{2n^4+4^n+2}}\)  solution 

(c) \(\displaystyle{\sum_{n=1}^{\infty} \frac{n-1}{3n \sqrt{n}}}\)   solution   

(d) \(\displaystyle{\sum_{n=1}^{\infty} \frac{2n^2-3n+5}{3n^4+5n^2+4n-3}}\)   solution 

(e) \(\displaystyle{\sum_{n=5}^{\infty} \frac{n+6}{(n+3)^{5}}}\)   solution

(f) \(\displaystyle{\sum_{n=1}^{\infty} \frac{7n+3^{n}}{2n+5^{n}}}\)   solution