Saturday, 12 July 2014

recurrence relations - Closed form for the sequence defined by a0=1 and an+1=an+a1n



Today, we had a math class, where we had to show, that a100>14 for



a0=1;an+1=an+a1n




Apart from this task, I asked myself: Is there a closed form for this sequence? Since I didn't find an answer by myself, can somebody tell me, whether such a closed form exists, and if yes what it is?


Answer



I agree, a closed form is very unlikely.
As for more precise asymptotics, I think an=2n+1/82ln(n)n11282(ln(n)2)2+o(1)n3/2


No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...