Dòng thứ 4 nhé

Đặt đại 1 cái tên kk 

\(N=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{107.109}+\frac{1}{109.111}\)

\(\Rightarrow2N=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{107.109}+\frac{2}{109.111}\)

\(\Rightarrow2N=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{109}-\frac{1}{111}\)

\(\Rightarrow2N=1-\frac{1}{111}\)

\(\Rightarrow2N=\frac{110}{111}\)

\(\Rightarrow N=\frac{55}{111}\)

ai đúng mình cho

ăăăăăăâê

Đáp án:

1/3-3/5+5/7-7/9+9/11-11/13+13/15+11/13-9/11+7/9-5/7+3/5-1/3

=(-1/3-1/3)+(5/7-(-5/7))+..........+(-11/13-11/13)+13/15

=0+0+...+0+13/15

=13/15

\(\frac{1}{3}-\frac{3}{4}+\frac{3}{5}+\frac{1}{14}-\frac{2}{9}-\frac{1}{36}+\frac{1}{15}\)

\(=\frac{1680-1260+1008+360-560-140+336}{5040}\)

\(=1424\)

\(\frac{1}{3}-\frac{3}{4}+\frac{3}{5}+\frac{1}{14}-\frac{2}{9}-\frac{1}{36}+\frac{1}{15}\)

\(\left(\frac{1}{3}+\frac{3}{5}+\frac{1}{15}\right)-\left(\frac{3}{4}+\frac{2}{9}+\frac{1}{36}\right)+\frac{1}{14}\)

\(=\left(\frac{5}{15}+\frac{9}{15}+\frac{1}{15}\right)-\left(\frac{27}{36}+\frac{8}{36}+\frac{1}{36}\right)+\frac{1}{14}\)

\(=1-1+\frac{1}{14}=\frac{1}{14}\)

\(\frac{1}{1}+\frac{1}{1}+\frac{1}{1}+\frac{1}{2}=\frac{2+2+2+1}{2}=\frac{7}{2}\)

1/1+1/1+1/1+1/2=(1/1x3)+1/2=3/1+1/2=7/2