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Sum of n terms 1x2+2x3+3x4+4x5+...

User KAK
by
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1 Answer

6 votes

Answer:

1/3(n+1)³

Explanation:

1x2+2x3+3x4+4x5+...= 1²+1+2²+2+3²+3+...+n²+n+1=

=(1²+2²+3²+...+n²)+(1+2+3+...+n+1)=

=1/6n(n+1)(2n+1)+1/2(n+1)(1+n+1)=

=1/6(n+1)(n(2n+1)+3(n+2))=

=1/6(n+1)(2n²+4n+2)=

=1/6(n+1)*2(n+1)²=

=1/3(n+1)³

User Jonathan Solorzano
by
9.0k points
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