Definition:
Several first sums:
- ,
- ,
- ,
- ,
- ,
- …
- ,
- ,
- ,
- ,
- ,
Related sums:
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- .
General dependency:
- .
More:
- = sum of squares of integer numbers, where the number of terms in the sum.
- = sum of squares of even numbers.
- = sum of squares of odd numbers.
- = sum of cubes of integer numbers
- = sum of cubes of even numbers.
- = sum of cubes of odd numbers.
- = sum of fourth degrees of integer numbers.
- = sum of fourth degrees of even numbers.
- = sum of fourth degrees of odd numbers.
- = sum of cubes of numbers starting with , finishing with with every two neighboring members of sequence spread apart .
Sources:
- T1989.02.14
- “Summing same degrees of subsequent natural numbers” by N.A. Andreyev (Matematical Education #5, Moskva 1960; pp. 201-202) (in Russian)