Ta có :
\(1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{16}\left(1+2+3+4+...+16\right)\)
\(=\)\(1+\frac{1}{2}.\frac{2\left(2+1\right)}{2}+\frac{1}{3}.\frac{3\left(3+1\right)}{2}+\frac{1}{4}.\frac{4\left(4+1\right)}{2}+...+\frac{1}{16}.\frac{16\left(16+1\right)}{2}\)
\(=\)\(1+\frac{2+1}{2}+\frac{3+1}{2}+\frac{4+1}{2}+...+\frac{16+1}{2}\)
\(=\)\(\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{17}{2}\)
\(=\)\(\frac{2+3+4+5+...+17}{2}\)
\(=\)\(\frac{\frac{16\left(17+2\right)}{2}}{2}\)
\(=\)\(\frac{152}{2}\)
\(=\)\(76\)
Bài này áp dụng công thức \(1+2+3+...+n=\frac{n\left(n+1\right)}{2}\) nhé
Chúc bạn học tốt ~
