A Series Built on a Recurrence
Difficulty: Medium · Topics: Calculus, Series, Sequences
Rekurrent munosabat asosidagi qator
The sequence \a n\ is defined by
a 1=1, a 2=2, a n+2=a n+1+a n (n=1,\ 2,\ 3,\ …).
What is the sum of the series Σ n=1^∞fraca na n+1a n+2?
\a n\ ketma-ketlik quyidagicha aniqlangan:
a 1=1, a 2=2, a n+2=a n+1+a n (n=1,\ 2,\ 3,\ …).
Σ n=1^∞fraca na n+1a n+2 qatorning yig‘indisi nechaga teng?