Question

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

Answer 1

9514 1404 393

Answer:

  $\displaystyle S_n=\sum_{k=1}^n{\frac{3^k}{3k-2}}$

Step-by-step 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 ...

  $\displaystyle \boxed{S_n=\sum_{k=1}^n{\frac{3^k}{3k-2}}}$