SOLUTION: Write the sum using summation notation, assuming the suggested pattern continues. 8 + 27 + 64 + 125 + ... + n3 choices below summation of n cubed from n equals 2 to inf

Algebra ->  Trigonometry-basics -> SOLUTION: Write the sum using summation notation, assuming the suggested pattern continues. 8 + 27 + 64 + 125 + ... + n3 choices below summation of n cubed from n equals 2 to inf      Log On


   

Question 1135686: Write the sum using summation notation, assuming the suggested pattern continues.
8 + 27 + 64 + 125 + ... + n3
choices below


summation of n cubed from n equals 2 to infinity

summation of the quantity n minus 1 cubed from n equals 2 to infinity

summation of the quantity n plus 1 cubed from n equals 2 to infinity

summation of n cubed from n equals 3 to infinity
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

8 = 2^3
27 = 3^3
64 = 4^3
125 = 5^3
and so on
In general, the last term n^3 indicates this pattern, as n is a whole number. The smallest n can be is n = 2. There is no upper limit on n, so it goes to infinity.

Therefore, the summation notation we write is

in terms of words, we would say
"Summation of n cubed from n equals 2 to infinity"

The use of summation notation written above is a compact way of writing
2^3 + 3^3 + 4^3 + 5^3 + ... + n^3

The fancy E looking symbol is the uppercase greek letter sigma (representing "S" in "Sum")

As you can probably guess, the number below the sigma tells you where n starts and the number up top tells you where you end, which in this case it doesn't end. The stuff to the right of sigma is the general expression we're adding, which you can think of as a template.