Question

Write in sigma notation 1/3,2/9,-7/27,14/81,-23/243,34/729...

Answer 1

Tricky. Note that the 1st term should be minus, but it is not. But it can be written as (-1)/(-3)

With that in mind, the numerators form the sequence

-1,2,7,14,23,34
where the 1st differences are
3,5,7,9,11 and the second differences are 2, meaning the numerators are a quadratic function: n^2-2

so the sum is

6
∑ (-1)^n * (n^2-2)/3^n
n=1

Answer 2

Thank you