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.

Printable View

- Jun 4th 2010, 05:53 AMtarheelbornSubsequence
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.

- Jun 4th 2010, 06:02 AMchisigma
The difference equation that produces the subsequence is...

$\displaystyle \Delta_{n}= a_{n+1} - a_{n}= 1+n$ , $\displaystyle a_{1}=1$ (1)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$ - Jun 4th 2010, 06:11 AMtarheelborn
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.

- Jun 5th 2010, 05:17 AMIdealconvergence
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