Help calculating a series \(\displaystyle{\sum_{{{n}={0}}}^{{4}}}{2}{n}\)

calcolare45pj

calcolare45pj

Answered question

2022-03-27

Help calculating a series
n=042n

Answer & Explanation

sorrisi7yny

sorrisi7yny

Beginner2022-03-28Added 9 answers

For this one you can use that
i=0ni3=(i=0n(i+1)3)(n+1)3
From here it is an easy computation to find the answer:
i=0ni3=i=0ni3+i=0n3i2+i=0n3i+i=0n1(n+1)3
which gives
i=0ni2=3n(n+1)2n1+n3+3n2+3n+13
i=0ni2=n33+n22+n6

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