Question

[Tran Toan]

Tính  M=1/3.8+1/8*13+1/13*18+...+1/33*38;

N=1/3*10+1/10*17+1/17*24+1/24*31+1/31+38

Answer 1

[Akai Haruma]

1/

$M=\frac{1}{3.8}+\frac{1}{8.13}+\frac{1}{13.18}+....+\frac{1}{33.38}$

$5M=\frac{8-3}{3.8}+\frac{13-8}{8.13}+\frac{18-13}{13.18}+...+\frac{38-33}{33.38}$

$=\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}+....+\frac{1}{33}-\frac{1}{38}$
$=\frac{1}{3}-\frac{1}{38}=\frac{35}{114}$

$\Rightarrow M=\frac{35}{114}:5=\frac{7}{114}$

Answer 2

[Akai Haruma]

2/

$N=\frac{1}{3.10}+\frac{1}{10.17}+\frac{1}{17.24}+\frac{1}{24.31}+\frac{1}{31.38}$

$7N=\frac{10-3}{3.10}+\frac{17-10}{10.17}+\frac{24-17}{17.24}+\frac{31-24}{24.31}+\frac{38-31}{31.38}$

$=\frac{1}{3}-\frac{1}{10}+\frac{1}{10}-\frac{1}{17}+\frac{1}{17}-\frac{1}{24}+\frac{1}{24}-\frac{1}{31}+\frac{1}{31}-\frac{1}{38}$

$=\frac{1}{3}-\frac{1}{38}=\frac{35}{114}$

$\Rightarrow N=\frac{35}{114}:7=\frac{5}{114}$