Question

Write the sigma notation for the infinite series27,9,3,1,1/3,1/9....

Answer 1

Given:

$27,9,3,1,\frac{1}{3},\frac{1}{9}...$

To write the sigma notation for the given infinite series, we first note the Infinite Geometric Series formula:

$\sum_{k\mathop{=}0}^{\infty}(ar^k)$

where:

r=common ratio

a=first term

We can get the common ratio by:

27(1/3)=9

9(1/3)=3

1(1/3)=1/3

Now, we can conclude that the common ratio is 1/3.

Therefore, the sigma notation for the given infinite series is:

$\sum_{k\mathop{=}0}^{\infty}27(\frac{1}{3})^k$