Question

Find a formula for the sequence 3, 9/4, 27/7, 81/10,... in sigma notation​

Answer 1

9514 1404 393

Answer:

`\displaystyle S_n=\sum_(k=1)^n{(3^k)/(3k-2)}`

Explanation:

The sequence terms appear to have numerators that are powers of 3, and denominators that are a linear (arithmetic) sequence with a first term of 1 and a common difference of 3.

numerator: 3^x

denominator: 1 +3(n -1) = 3n-2

Then the sum of n terms of the sequence can be described by ...

`\displaystyle \boxed{S_n=\sum_(k=1)^n{(3^k)/(3k-2)}}`