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

debos

New member
Joined
Jul 3, 2019
Messages
7
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.
 
The second sum is of the form:

[MATH]S=\sum_{k=1}^{10}\left((2k)^3\right)[/MATH]
If we factor, as I suggested, we get:

[MATH]S=2^3\sum_{k=1}^{10}\left(k^3\right)[/MATH]
Can you proceed, using the information given in the problem regarding the second factor, which is a sum?
 
The second sum is of the form:

[MATH]S=\sum_{k=1}^{10}\left((2k)^3\right)[/MATH]
If we factor, as I suggested, we get:

[MATH]S=2^3\sum_{k=1}^{10}\left(k^3\right)[/MATH]
Can you proceed, using the information given in the problem regarding the second factor, which is a sum?
Yes, clear now. Thank you.
 
Top