0
votes
2answers
202 views

sequences - recurrence relation [closed]

I have to find the expression of $(y_n)$ defined by : $$y_{n+1}=a y_n+b z_n+c$$ where $(z_n)$ is an arithmetico-geometric sequence : $$z_{n+1}=d z_n+e$$ and $a,b,c,d,e$ real numbers. Thank you ...
2
votes
2answers
583 views

Sum of Series Where Exponent is Sum of Arithmetic Progression

Hi, How do i get the sum of such a sequence: $1 + x^{-1} + x^{-3} + x^{-6} + ...$ where the exponents are actually sum of arithmetic progression. i.e. $x^{-0} + x^{-(0 + 1)} + x^{-(0 + 1 + 2)} + ...