Mình biết làm này nhưng sợ bạn ko hiểu
nhớ tk cho mk bài này như sau:
1/2.[2/3.5+2/5.7+2/7.9+...+2/(2x+1).(2x+3)]=15/93
1/2.[1.3-1/5+1/5-1/7+1/7-1/9+...+1/(2x+1)-1/(2x+3)]=5/31(rút gọn)
1/3-1/(2x+3)=5/31:1/2
1/3-1/(2x+3)=10/31
1/2x+3=1/3-10/31
1/2x+3=1/93
=>2x+3=93
2x=93-3
2x=90
x=90:2
x=40
Vậy x=40
Từ đề bài ta có:1/2.(2/3.5+2/5.7+2/7.9+...+2/(2x+1)(2x+3) = 15/93
1/2(1/3-1/5+1/5-1/7+1/7-1/9+...+1/2x+1-1/2x+3) = 15/93
1/3-1/2x+3 = 15/93:1/2=10/31
1/2x+3 = 1/3-10/31=1/93
suy ra : 2x+3 = 93
2x = 93 - 3= 90
x= 90:2=45
vậy x=45
Ta có:
\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{\left(2x+1\right).\left(2x+3\right)}=\frac{15}{93}\)
\(\Rightarrow\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{\left(2x+1\right)\left(2x+3\right)}=\frac{15}{93}\)
\(\Rightarrow2\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{\left(2x+1\right)\left(2x+3\right)}\right)=\frac{15}{93}\)
\(\Rightarrow\frac{1}{3}-\frac{1}{\left(2x+3\right)}=\frac{15}{93}:2\)
\(\Rightarrow\frac{1}{3}-\frac{1}{\left(2x+3\right)}=\frac{5}{62}\Leftrightarrow\frac{1}{2x+3}=\frac{1}{3}-\frac{5}{62}=\frac{47}{186}\)
Áp dụng tỉ lệ thức:
\(\frac{1}{2x+3}=\frac{47}{186}\Leftrightarrow1.186=47.\left(2x+3\right)\)
\(\Rightarrow x=\left(\frac{186}{47}-3\right):2=\frac{45}{94}\)
Mình không biết đúng không nữa.
olgoholhi
