Question

Express the series using sigma notation.
-6m – 3m + 0 + 3m + 6m ...

Answer 1

n = ∞
∑ 3m n
n = -∞

Its been a while but I think that's correct

Answer 2

∞

∑ 3m-3

n=1

Explanation:

The first thing you need to know is if the series is arithmetic or an arithmetic sequence or a geometric sequence. Since we have a common difference between the series, this sequence is arithmetic. In this particular case, you can see it increases in 3m every time.

To solve this, we need to write the general equation for arithmetic sequences:
`a_(n) = a_(i)+(n-1)d` then replace it with values given, beign
`a_(i)` the initial value of the series (In this case, -6m), and d is the common difference between series values, which is 3.

• Replacing the values we get
  `a_(n)=-6m+(nm-1)*3`
• 
  `a_(n)=-6m+9m-3`
• 
  `a_(n)=3m-3`

So to express the series using sigma notation, we get

∑3m-3 starting in n=1 to ∞

Have a nice day.