A=1+1/2x3+1/3X6+1/4X10+...+1/16X136
A=1+3/2+2+5/2+3+...+17/2
A=2/2+3/2+4/2+5/2+6/2+...+17/2
A=2+3+4+5+...+16+17/2
A=(2+17)x16:2/2
A=19x16:2/2
A=304:2/2
A=152/2
A=76
M = 1+3/2+6/2+.....+136/16
= 2/2+3/2+4/2+.....+17/2
= 2+3+....+17/2
= 152/2
= 76
Tk mk nha
\(\text{M}=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{16}\left(1+2+3+...+16\right)\)
Xét \(\text{M}=1+2+3+4+5+...+\text{n}=\frac{\left(\text{n}+1\right)\text{n}}{2}\)lấy \(\frac{\text{S}}{\text{n}}=\frac{\frac{\left(\text{n}+1\right)\text{n}}{2}}{\text{n}}=\frac{\text{n}+1}{2}\)
Ta có: \(\text{M}=1+\frac{\frac{2\left(2+1\right)}{2}}{2}+\frac{\frac{3\left(3+1\right)}{2}}{3}+\frac{\frac{4\left(4+1\right)}{2}}{4}+\frac{\frac{5\left(5+1\right)}{2}}{5}+...+\frac{\frac{16\left(16+1\right)}{2}}{16}\)
\(\text{M}=1+\frac{1+2}{2}+\frac{1+3}{2}+\frac{1+4}{2}+\frac{1+5}{2}+...+\frac{1+16}{2}\)
\(\text{M}=1+\frac{1+2+1+3+1+4+1+5+1+6+...+1+16}{2}\)
\(\text{M}=1+\frac{151}{2}\)
\(\text{M}=\frac{153}{2}\)
\(M=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{16}\left(1+2+3+...+16\right)\)
\(=1+\frac{1}{2}.\frac{2.3}{2}+\frac{1}{3}.\frac{3.4}{2}+...+\frac{1}{16}.\frac{16.17}{2}\)
\(=1+\frac{3}{2}+\frac{4}{2}+...+\frac{17}{2}\)
\(=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+...+\frac{17}{2}\)
\(=\frac{2+3+4+...+17}{2}\)
\(=\frac{152}{2}\)
\(=76\)
Study well ! >_<
