Question

Help me : Tính:

     A=1+1/2(1+2)+1/3(1+2+3)+.......+1/16(1+2+3+....+16)

 

Answer 1

\(A=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{16}\left(1+2+...+16\right)\)

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

\(=1+\frac{3}{2}+\frac{4}{2}+...+\frac{17}{2}\)

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

\(=\frac{1}{2}\left(\frac{16\left(17+2\right)}{2}\right)=\frac{1}{2}.152=76\)