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)