- #1
aalmighty
- 17
- 0
It's a nice li'l series. The question is to find an expression for the series
S=1^3-2^3+3^3-4^3+...-(2m-2)^3+(2m-1)^3
where m is a subset of N
I added and subtracted sum of even squares to get
S={1^3+2^3+3^3+4^3+...+(2m-1)^3}-{2(2^3+4^3+6^3+...+(2m-2)^3)}
Replaced the first part by [(2m-1)(2m)/2]^2 to get
S=[(2m-1)(2m)/2]^2-2(2^3+4^3+6^3+...+(2m-2)^3)
now All I need to complete the problem is to get the general formula for the sum of cubes of the first n even natural numbers, plug the values and evaluate. Can anyone please help?
Also, Please let me know if there is an alternative way to solve this problem.
S=1^3-2^3+3^3-4^3+...-(2m-2)^3+(2m-1)^3
where m is a subset of N
I added and subtracted sum of even squares to get
S={1^3+2^3+3^3+4^3+...+(2m-1)^3}-{2(2^3+4^3+6^3+...+(2m-2)^3)}
Replaced the first part by [(2m-1)(2m)/2]^2 to get
S=[(2m-1)(2m)/2]^2-2(2^3+4^3+6^3+...+(2m-2)^3)
now All I need to complete the problem is to get the general formula for the sum of cubes of the first n even natural numbers, plug the values and evaluate. Can anyone please help?
Also, Please let me know if there is an alternative way to solve this problem.