Question

Bài 3: Tính 

A = ( 1 + 2 ) . 1/2 + ( 1 + 2 + 3 ) . 1/3 + ... + ( 1 + 2 + 3 +...+ 2016) . 1/2016

Answer 1

\(A=\left(1+2\right).\frac{1}{2}+\left(1+2+3\right).\frac{1}{3}+...+\left(1+2+3+...+2016\right).\frac{1}{2016}\)

\(A=\left(1+2\right).2:2.\frac{1}{2}+\left(1+3\right).3:2.\frac{1}{3}+...+\left(1+2016\right).2016:2.\frac{1}{2016}\)

\(A=3:2+4:2+...+2017:2\)

\(A=3.\frac{1}{2}+4.\frac{1}{2}+...+2017.\frac{1}{2}\)

\(A=\frac{1}{2}.\left(3+4+...+2017\right)\)

\(A=\frac{1}{2}.\left(3+2017\right).2015:2\)

\(A=\frac{1}{2}.2020.2015.\frac{1}{2}\)

\(A=505.2015=1017575\)