Answer :

1. You have that the series is: 5+25+125+625+3125+15625
2. You must find the ratio (r) between the adjacent members. Then, you have:

25/5=5
125/25=5
625/125=5
3125/625=5
15625/3125=5

3. Therefore, the ratio is:

r=5

4. Then, each term has te form 5^k. So, you have:

5^1=5
 5^2=25
 5^3=125
 5^4=625
 5^5=3125
 5^6=15625

5. As you can see, "k" goes from 1 to 6.

6. The answer is shown in the image attached.

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Rewritten by : Barada

Final answer:

The series 5+25+125+625+3125+15625 can be rewritten in sigma notation as Σ 5*5^(n-1) from n=1 to 6, representing a geometric series with a common ratio of 5 and 6 terms.

Explanation:

To rewrite the series 5+25+125+625+3125+15625 using sigma notation, we first need to identify the pattern of the series. We notice that each term is 5 times the previous term, which is a characteristic of a geometric series. A geometric series can be expressed in sigma notation as Σ a*r^(n-1) from n=1 to N, where a is the first term, r is the common ratio between terms, and N is the number of terms.

In this series, a = 5, and r = 5. The series has 6 terms, so N = 6. Therefore, the series in sigma notation is Σ 5*5^(n-1) from n=1 to 6.