[SOLVED] MA1023 Homework 3

In exercise 1-4, determine the convergence or divergence of the series. If the series is convergent, find the sum value.

1.

n +      3n

2

n=1

2. – _∞

X (⁻2)ⁿ 3n+1₋ 4n n=1

3. ∞ ∞

X n X 2 1)         2) cos( ) n+1    n n=1      n=1

4. ∞

X (⁻2)n                                       

1) n+ 3n 2) ₅n n=1      n=1

In exercise 5-6, determine the convergence or divergence of the series. Specify the test you use in determining the convergence or divergence of the series.

5.

1)                    2)

n=1n²                                                         n=1 3

6. ∞ ∞

X                                          X n+1

1) 2) n3 +1 nn=1

In exercise 7-8, use ratio test to determine the convergence or divergence of the series.

7. ∞

X 2n+1

n3n−1 n=1

8. ∞

X n2

(−4)n n=1