value of series 2^3+4^3+6^3+........+20^3

debos

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if 1^3+2^3+3^3+4^3................+10^3=3025,then find the value of series 2^3+4^3+6^3+........+20^3.
 

MarkFL

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What happens if you factor out \(2^3\) from the second sum?
 

debos

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MarkFL

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The second sum is of the form:

\(\displaystyle S=\sum_{k=1}^{10}\left((2k)^3\right)\)

If we factor, as I suggested, we get:

\(\displaystyle S=2^3\sum_{k=1}^{10}\left(k^3\right)\)

Can you proceed, using the information given in the problem regarding the second factor, which is a sum?
 

debos

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Jul 3, 2019
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The second sum is of the form:

\(\displaystyle S=\sum_{k=1}^{10}\left((2k)^3\right)\)

If we factor, as I suggested, we get:

\(\displaystyle S=2^3\sum_{k=1}^{10}\left(k^3\right)\)

Can you proceed, using the information given in the problem regarding the second factor, which is a sum?
Yes, clear now. Thank you.
 
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