a,  ( 1/2 + 1) . ( 1/3 + 1) . (1/4 + 1) ... ( 1/999 + 1)

= 3/2 . 4/3 . 5/4 . 1000/999

= 1/2 . 1/1 . 1/1 ... 1000/1

= 1000/2 

= 500

b, (1/2-1) . (1/3-1) . (1/4-1) ... (1/1000-1)

= -1/2 . (-2)/3 . (-3)/4 ... (-999)/1000

= (-1)/1 . (-1)/1 . (-1)/1 ... (-1)/1000

= (-1)/1000

c, 3/2^2 . 8/3^2 . 15/4^2 ... 99/10^2

= 1.3/2.2 * 2.4/3.3 * 3.5/4.4***9.11/10.10

=( 1.2.3...99).(3.4.5...11)/(2.3.4....10).(2.3.4...10)

= 1.11/2.10

= 11/20

Nếu ko cần trình bày thì dùng Pascal mà làm

a,\(\left(\dfrac{1}{2}+1\right)\left(\dfrac{1}{3}+1\right)\left(\dfrac{1}{4}+1\right)...\left(\dfrac{1}{999}+1\right)\)

\(=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}.....\dfrac{1000}{999}\)

\(=\dfrac{3.4.5....1000}{2.3.4....999}=\dfrac{1000}{2}=500\)

b,\(\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)\left(\dfrac{1}{4}-1\right)...\left(\dfrac{1}{1000}-1\right)\)

\(=\dfrac{-1}{2}.\dfrac{-2}{3}.\dfrac{-3}{4}.....\dfrac{-999}{1000}\)

=\(\dfrac{-\left(1.2.3....999\right)}{2.3.4....1000}=\dfrac{-1}{1000}\)

c,\(\dfrac{3}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}....\dfrac{99}{10^2}\)

\(=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}....\dfrac{9.11}{10.10}\)

\(=\dfrac{1.3.2.4.3.5....9.11}{2.2.3.3.4.4....10.10}\)

\(=\dfrac{1.2.3...9}{2.3.4...10}.\dfrac{3.4.5...11}{2.3.4...10}\)

\(=\dfrac{1}{10}.\dfrac{11}{2}=\dfrac{11}{20}\)

Giải chi tiết hộ luôn với 

a)   =3/2*4/3*5/4*....* 1000/999

     =3*4*5*......*1000 / 2*3*4*...*999

     =1000/2=500

phần b;c mk chưa làm đc

a. =3/2*4/3*5/4*...*1000/999

=3*4*5*....*1000/2*3*4*...*999

=1000/2

=500

b. =-1/2*-2/3*-3/4*....*-999/1000

=-1*-2*-3*.....*-999/2*3*4*....*1000

=-1/1000

Mk cũng đồng ý

b) ...........

= 1/2x2/3x.....x999/1000

= 1x2x...x999/2x3x...x1000

=1/1000

a) ...............

= 3/2 . 4/3 .... 1000/999

= 3x4x5x....x1000/2x3x4x...x999

=1000/2=500

bạn k cho mik rồi mik mới trả lời

Câu 11:

(\(\dfrac{11}{4}\). \(\dfrac{-5}{9}\) - \(\dfrac{4}{9}\).\(\dfrac{11}{4}\)).\(\dfrac{8}{33}\)

= \(\dfrac{11}{4}\).(\(\dfrac{-5}{9}\)  - \(\dfrac{4}{9}\)). \(\dfrac{8}{33}\)

= \(\dfrac{11}{4}\).(-1).\(\dfrac{8}{33}\)

= - \(\dfrac{2}{3}\)