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Answer :
The sum 1+5+25+125+625+3125 is a geometric series that can be represented in sigma notation as
cent;_(i=0)^5 5^i. This notation efficiently encapsulates the series with a first term of 1 and a common ratio of 5.
The sum 1+5+25+125+625+3125 is a geometric series with a common ratio of 5. To write this sum in sigma notation, we identify the first term and the common ratio. The first term is 1 (which is 50), and each subsequent term is the previous term multiplied by 5. Therefore, the ith term can be expressed as 5i where i starts from 0 and goes up to 5.
The sigma notation for this sum is:
cent;_(i=0)^5 5i
A step-by-step explanation starts with recognizing the pattern of multiplication by 5 to obtain the next term. We then determine the exponent for each term, starting from 0, since 50 = 1. Finally, we use the sigma notation, with the summation index i starting from 0 and ending at 5, multiplying 5 to the power of i. This compactly represents the original sum.
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