Question

Which of the following statements is true for the sequence with general term a sub n equals the quotient of the product of the quantities negative 1 raised to the n plus 1 power and n over the quantity 2 times n plus 1 , for

n = 1, 2, 3…? (10 points)

A) It is decreasing.
B) It is oscillating.
C) It is convergent.
D) It is bounded above but not bounded below.

Answer 1

why not use math, instead of words?

a_n = (-1)^(n+1) * n/(2(n+1))

well, B is certainly true.
What about the ratio test?

((n+1)/(2((n+1)+1)))/(n/(2(n+1))) = (n+1)^2 / (n^2+2) > 1 for n>0

so now what?