Question

tính : C = 1.4 + 2.5 + 3.6 + 4.7 + … + n(n + 3)

Answer 1

\(C=1.4+2.5+...+n(n+3)\)

\(=1(1+3)+2(2+3)+...+n(n+3)\)

\(=1^2+3.1+2^2+3.2+...+n^2+3.n\)

\(=(1^2+2^2+...+n^2)+3(1+2+...+n)\)

\(=\dfrac{n(n+1)(2n+1)}{6}+3.\dfrac{n(n+1)}{2}\)

\(=\dfrac{n(n+1)}{2}.\begin{pmatrix} \dfrac{2n+1}{3}+3 \end{pmatrix}\)

\(=\dfrac{n(n+1)(2n+10)}{6}=\dfrac{n(n+1)(n+5)}{3}\)

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