Question

Thực hiện tính :

M= 1+\(\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}.\left(1+2+3\right)+\dfrac{1}{4}\left(1+2+3+4\right)+....+\dfrac{1}{16}\left(1+....16\right)\)

(Giải thích rõ giùm mk vs nhá - thanks)

Answer 1

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

\(=1+\dfrac{1}{2}\cdot\dfrac{2\cdot3}{2}+\dfrac{1}{3}\cdot\dfrac{3\cdot4}{2}+...+\dfrac{1}{16}\cdot\dfrac{16\cdot17}{2}\)

\(=\dfrac{2}{2}+\dfrac{3}{2}+\dfrac{4}{2}+\dfrac{5}{2}+...+\dfrac{16}{2}+\dfrac{17}{2}\)

\(=\dfrac{1}{2}\left(2+3+4+5+...+17\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{\left(17+2\right)\cdot16}{2}=76\)