What is the sum of the first n terms of the sequence {n * (n + 2)}? Talk more about ideas,

What is the sum of the first n terms of the sequence {n * (n + 2)}? Talk more about ideas,

solution
n(n+2)=n²+2n
∴sn
=(1²+2²+3²+…… +n²)+2(1+2+3+…… +n)
=n*(n+1)*(2n+1)/6+2×(1+n)n/2
=1/6n(n+1)(2n+1)+(1+n)n
=n(n+1)(1/3n+1/6+1)
=n(n+1)(1/3n+7/6)
Formula 1 & # 178; + 2 & # 178; + +n²=n*(n+1)*(2n+1)/6

Elden Ring Premiere

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