t1=0, find the first few terms tn=1/tn-1+2, what is the pattern?
Hello, nithujaa!
Given: .
Find the first few terms. .What is the pattern?
The fractions are: .
The numerators form the sequence: .
The denominators are "one step ahead."
For the numerators, we have: .
. . Each term is twice the preceding term, plus the second preceding term.
If you require a "closed form" for the numerators, here it is:
. .