\(\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{180}=\frac{1}{2}.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\right)=\frac{1}{2}.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)\(=\frac{1}{2}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)=\frac{1}{2}.\left(1-\frac{1}{10}\right)=\frac{1}{2}.\frac{9}{10}=\frac{9}{20}\)

1. Cho phân số a/b, b>a. C/m :

a) Nếu a/b < 1 thì a+1/b+1 > a/b

b) Nếu a/b > 1 thì a/b > a+1/b+1

2. Tính :

3/4 + 3/12 + 3/24 + 3/40 + 3/60 + 3/84 + 3/112 + 3/144 + 1/180

Toán lớp 6

\(=20,15\times\left(23+76+1\right)=20,15\times100=2015\)

=20,15x(23+76+1)

=20,15x100

=2015

Đây nha

=20,15x(23+76+1)

=20,15x100=2015

2A=1/2+1/6+1/12+1/20+1/30+1/42

    =1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7

    =1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7

    =1-1/7

    =6/7

\(A=\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+\frac{1}{40}+\frac{1}{60}+\frac{1}{84}\)NHÂN CẢ TỬ VÀ MẪU CỦA TỪNG P/S VỚI 2 TA ĐƯỢC:

\(A=\frac{2}{8}+\frac{2}{24}+\frac{2}{48}+\frac{2}{80}+\frac{2}{120}+\frac{2}{168}\)

\(A=\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{12.14}\)

\(A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{12}-\frac{1}{14}\)

\(A=\frac{1}{2}-\frac{1}{14}\)

\(A=\frac{3}{7}\)

Giá trị của biểu thứu A là 3/7

ta có: A = 1/4 + 1/12 + 1/24 + 1/40 + 1/60 + 1/84

            = 2 ( 1/2*4 + 1/4*6 + 1/6*8 + 1/8*10 + 1/10*12 + 1/12*14 )

            = 2 ( 1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + 1/8 - 1/10 + 1/10 - 1/12 + 1/12 - 1/14 )

            = 2 ( 1/2 - 1/14 )

            = 6/7

Tính tổng sau:

1/4+1/12+1/24+....+1/1300