The nth term of a sequence is n/n+1. What is the expression for the difference between the (n+1)th term and the nth term?

Answer:

7) B

nth term = n/(n+1)

So, (n + 1)th term:

n + 1
n+1+1

n + 1
n + 2

Difference between (n + 1)th term and nth term:

n + 1 – n
n +2 n + 1

n + 1 (n + 1) – n (n +2)
(n + 2) (n + 1)

n² + 2n + 1 – n² – 2n
(n + 2) (n + 1)

1/(n+2) (n+1)