If you have a sequence which is not geometric or arithmetic, is there any methodology to follow in order to have a formula for its sum ?

Take for example the following sequence: \(\displaystyle \{0.9^{\frac{1}{2}(n-i+1)(i+n)}\}_{i=1}^n\). It is not a geometric or an arithmetic progression. I don't see how to split it into sums of sequences which are arithmetic or geometric. Is there any hints I can get to proceed with writing a formula for this sum ?

\(\displaystyle S_n = \sum_{i=1}^n 0.9^{\frac{1}{2}(n-i+1)(i+n)} \)

Take for example the following sequence: \(\displaystyle \{0.9^{\frac{1}{2}(n-i+1)(i+n)}\}_{i=1}^n\). It is not a geometric or an arithmetic progression. I don't see how to split it into sums of sequences which are arithmetic or geometric. Is there any hints I can get to proceed with writing a formula for this sum ?

\(\displaystyle S_n = \sum_{i=1}^n 0.9^{\frac{1}{2}(n-i+1)(i+n)} \)

Last edited by a moderator: