Finding the Value of a Series: Help with (h) and Power of r | Homework Question

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The discussion focuses on finding the value of a series involving terms with powers of r. Participants suggest using different approaches for the summation components, specifically recommending the use of partial sums for both arithmetic and geometric sequences. For the term involving 4r, the arithmetic sequence method is advised, while the geometric sequence method is suggested for the term with 3.2r. The original poster seeks clarification on the appropriate formulas to apply for these calculations. Understanding the distinction between arithmetic and geometric series is crucial for solving the problem effectively.
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Homework Statement



Find the value of the following series: i need help with (h). Thanks...
DSC00555.jpg


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The Attempt at a Solution



I don't know which formula to use for this type of question (with power of r), can anyone enlighten me?
 
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For the part of the summation involving 4r, use the partial sums of an arithmetic sequence.

For the part of the summation involving 3.2r, use the partial sums of a geometric sequence.
 

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