Summation notation

Question

rewrite the series using summation notation. Use 1 as the lower limit or summation.

 

-1/3+1/6-1/9+...+1/18

(Type the expression using i as the variable)

Answer 1

 6

 ∑ [(-1)ⁱ/(3i)]
 i=1

 

Jim explained how the summation comes to be.

Above is how it looks.

Answer 2

Hi Lauren,

 

This question will be a challenge to answer clearly because there is no way to insert complex mathematical notation.  So, fingers crossed.

 

The sum has a total of 6 terms.  If we write the entire sum fully, it is:

 

-1/3 + 1/6 - 1/9 + 1/12 - 1/15 + 1/18

 

Notice the denominators are simply multiples of 3, so the sum can be written as 

 

-1/(3*1) + 1/(3*2) - 1/(3*3) + 1/(3*4) - 1/(3*5)+ 1/(3*6)

 

So, the first part of the summation is the large sigma Σ.  Underneath the sigma is an i = 1 and the above the sigma is a 6. 

 

The equation after the sigma should be (-1)^i  *  1/3i

 

The (-1)^i is the piece that alternates the signs between negative and positive

The 1/3i gives us the rest of the terms.

 

Hope this helps!!  :)