\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{9999}{10000}\)

\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{99.101}{100.100}\)

\(=\frac{1.2.3....99}{2.3.4....100}.\frac{3.4.5....101}{2.3.4...100}\)

\(=\frac{1}{100}.\frac{101}{2}=\frac{101}{200}\)

\(B=\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).....\left(1-\frac{1}{10000}\right)\)

\(=\frac{3}{4}.\frac{8}{9}....\frac{9999}{10000}=\frac{101}{200}\)

gọi số phải tìm là A   A
=(1.3).(2.4).(3.5)...(99.101)/
(2².3².4²...100²)

=(1.2.3...99).(3.4.5...101)/
[(1.2.3.4...100)(2.3.4...100)]

=101/(100.2)=101/200

D=1.3/2.2 . 2.4/3.3 . 3.5/4.4 ..... 99.101/100.100

D=1.2.3.....99/2.3.4.....100 . 3.4.5.....101/2.3.4.....100

D=1/100 . 101/2

D=101/200

\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{9999}{10000}\)

\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{99.101}{100.100}\)

\(A=\frac{1.2.3...99}{2.3.4...100}.\frac{3.4.5...101}{2.3.4...100}=\frac{1}{100}.\frac{101}{2}=\frac{101}{200}\)

3/4.8/9.15/16......9999/10000
= 3.8.15.....9999/4.9.16......10000
=101/50

a; \(\dfrac{5}{6}\) + \(\dfrac{5}{12}\) + \(\dfrac{5}{20}\) + ... + \(\dfrac{5}{132}\)

 = 5.(\(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\) + ..+ \(\dfrac{1}{132}\))

= 5.(\(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + ... + \(\dfrac{1}{11.12}\))

= 5.(\(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + ...+ \(\dfrac{1}{11}\) - \(\dfrac{1}{12}\))

= 5.(\(\dfrac{1}{2}\) - \(\dfrac{1}{12}\))

= 5.(\(\dfrac{6}{12}\) - \(\dfrac{1}{12}\))

= 5.\(\dfrac{5}{12}\)

= \(\dfrac{25}{12}\)

b; \(\dfrac{1}{2.4}\) + \(\dfrac{1}{4.6}\) + ... + \(\dfrac{1}{x.\left(x+2\right)}\)

= \(\dfrac{1}{2}\) .(\(\dfrac{2}{2.4}\) + \(\dfrac{2}{4.6}\) + ... + \(\dfrac{2}{x\left(x+2\right)}\))

= \(\dfrac{1}{2}\).(\(\dfrac{1}{2}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{6}\) +...+ \(\dfrac{1}{x}\) - \(\dfrac{1}{x+2}\))

= \(\dfrac{1}{2}\).(\(\dfrac{1}{2}\) - \(\dfrac{1}{x+2}\))

= \(\dfrac{1}{2}\).\(\dfrac{x+2-2}{x+2}\)

= \(\dfrac{x+\left(2-2\right)}{2.\left(x+2\right)}\)

= \(\dfrac{x+0}{2\left(x+2\right)}\)

= \(\dfrac{x}{2.\left(x+2\right)}\)

A = \(\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot\cdot\cdot\cdot\frac{9999}{10000}=\frac{1\cdot3}{2.2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\frac{3.5}{4.4}\cdot\cdot\cdot\cdot\frac{99\cdot101}{100\cdot100}=\frac{1}{2}\cdot\frac{101}{100}=\frac{101}{200}\)

B = ( 1- 1/4 )( 1-1/9) ...( 1-1/10000 ) = 3/4 . 8/9 .....9999/100000 ( tương tự A )

a=5051/100 co ma

xin loi ban lam dung roi minh nham