series and sequence

Question

Q1: What is the 3rd term of {n+1/3n+1} n=1 to n=inf

Q2: What is the sum of the geometric series n=1 to inf 2/3^n

Q3: Which of the following is true for the series n=1 to inf 1/n^4/5 (multiple choice)

a-none of the above

b-divergent p series

c-convergent geometric series

d-convergent p series

e-divergent geometric series

Answer 1

(n+1)/(3n+1)

1st term is: 2/4 = 1/2

2nd term is 3/7

3rd term is: (3+1)/(3x3+1) = 4/10 = 2/5

4th term is: (4+1)/(3x4+1) = 5/13

1/2, 3/7, 2/5, 5/13, ....

Unless you intended n+ (1/3)n + 1, then

1st term: 1+1/3+ 1 = 2 1/3

2nd term 2+ 2/3 + 1 = 3 2/3

3rd term: 3 + 3/3 + 1 = 5

or maybe you meant n+ 1/3n + 1, then

1st term 1+1/3 + 1 = 2 1/3

2nd term: 2 + 1/6 + 1 = 3 1/6

3rd term: 3 + 1/9 + 1 = 4 1/9

Best guess is you intended the 1st of these 3 possibilities, although lack of parentheses makes the other two more technically correct. Depending on which was intended changes the answers to the remaining parts of the problem.