Answer:
summation of five times negative three to the power of n from n equals zero to infinity
Step-by-step explanation:
Summation Notation
It represents the sum of a finite or infinite number of terms. Let's analyze the terms of the given succession:
5-15+45-135+...
If we take 5 as a common factor, we have
5(1-3+9-27+...)
The parentheses contain the alternate sum/subtraction of powers of 3. The odd terms are positive, the even terms are negative, thus the exponent must be n starting from 0 or n-1 starting from 1
The summation is then represented by
[tex]\sum_{n=0}^{\infty}5(-3)^n[/tex]
This corresponds with the option:
summation of five times negative three to the power of n from n equals zero to infinity
