MHB Serina's questions at Yahoo Answers regarding sigma notation

AI Thread Summary
The discussion addresses Serina's questions about expressing two series in summation notation. The first series, 4 - 24 + 144 - 864 + ..., can be represented as S = 4∑(-6)^k from k=0 to infinity. The second series, 729 + 1000 + 1331 + 1728 + ... + n^3, is expressed as S = ∑k^3 from k=9 to n. The responses provide clear mathematical formulations for both series. Participants are encouraged to share additional pre-calculus problems for further discussion.
MarkFL
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Hello serina,

1.) I would begin by observing the series can be written as:

$$S=4(-6)^0+4(-6)^1+4(-6)^2+\cdots$$

and so we have:

$$S=4\sum_{k=0}^{\infty}(-6)^k$$

2.) I would begin by observing the series can be written as:

$$S=9^3+10^3+11^3+12^3+\cdots+n^3$$

and so we have:

$$S=\sum_{k=9}^n k^3$$

To serina and any other guests viewing this topic, I invite and encourage you to post other pre-calculus problems here in our http://www.mathhelpboards.com/f21/ forum.

Best Regards,

Mark.
 
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