Thread: Subsequence

Is {1, 3, 6, 10, 15, ...} a subsequence of the natural numbers and, if so, what function composed with the natural numbers gives this subsequence? Thanks.

The difference equation that produces the subsequence is...

, (1)

Kind regards

I am not sure how to make this work with what I have. I have the composition of f and g = [n(n+1)]/2 = {1, 3, 6, 10, 15, ...}. I know that f = {1, 2, 3, 4, ...}. I need to find g.

Let f(1)=1, f(2)=3, f(3)=6, f(4)=10, f(5)=15 and so on. Then

f(1)=1
f(2)-f(1)=2
f(3)-f(2)=3
f(4)-f(2)=4
...............
f(n)-f(n-1)=n

Adding these f(n)=n(n+1)/2