Question

Tính nhanh: 1+1/2×(1+2)+1/3×(1+2+3)+1/4×(1+2+3+4)+...+1/16×(1+2+3+...+16)

Answer 1

\(1+\dfrac{1}{2}.\left(1+2\right)+\dfrac{1}{3}.\left(1+2+3\right)+...+\dfrac{1}{16}\left(1+2+3+...+16\right)\)

\(=1+\dfrac{1}{2}.\dfrac{2.3}{2}+\dfrac{1}{3}.\dfrac{3.4}{2}+...+\dfrac{1}{16}.\dfrac{16.17}{2}\)

\(=\dfrac{2}{2}+\dfrac{3}{2}+\dfrac{4}{2}+...+\dfrac{17}{2}\)

\(=\dfrac{1}{2}\left(2+3+4+...+17\right)\)

\(=76\)