If $a_n=(a_{n-1}+a_{n-2})/2$ and $a_1, a_2$ are given, will this series converge? And if so, what is the limit?
By intuition I think it converges to $(a_1+2a_2)/3$ , but I am not able to prove it.
2026-02-23 20:40:56.1771879256
Will this series converge? If so, what is its limit?
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We have $$2a_n-a_{n-1}-a_{n-2}=0$$
Using Recurrence Relation formula , $$a_n=A+B\left(-\frac12\right)^n$$