oi baka

A = 13/21.2/11 + 13/21.9/11 + 8/21
= (13/21) + (13/21) + (8/21)
= (13 + 13 + 8)/21
= 34/21

B = (1 - 1/5)(1 - 2/5)(1 - 3/5)...(1 - 9/5)
= (4/5)(3/5)(2/5)(1/5)(0/5)(-1/5)(-2/5)(-3/5)(-4/5)
= 0

C = (1 - 1/2)(1 - 1/3)(1 - 1/4)...(1 - 1/50)
= (1/2)(2/3)(3/4)(4/5)...(49/50)
= 1/50

D = (2^2/1.3) * (3^2/2.4) * (4^2/3.5) * (5^2/4.6) * (6^2/5.7)
= (4/3) * (9/8) * (16/15) * (25/23) * (36/35)
= 0.979

Nhầm ,chỉ có một + 1/3.5 thôi các bạn nhé

https://hoc24.vn/hoi-dap/question/598367.html

a: \(A=\dfrac{1}{2}\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+...+\dfrac{2}{2022\cdot2024}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{2022}-\dfrac{1}{2024}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{1011}{2024}=\dfrac{1011}{4848}< \dfrac{1}{4}\)

b: \(B=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{2013\cdot2015}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2013}-\dfrac{1}{2015}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{2014}{2015}=\dfrac{1007}{2015}< \dfrac{1}{2}\)

A = 1.100 + 2.99 + 3.98 + 98.3 + 99.2 + 100.1

1.100 = 1.100 = 1.100

2.99 = 2.(100 - 1) = 2.100 - 1.2

3.98 = 3.(100 - 2) = 3.100 - 2.3

4.97 = 4.(100 - 3) = 4.100 = 3.4

...............................................................

100.1 = 100.(100 - 99) = 100.100 - 99.100

Cộng vế với vế ta có:

A = 1.100+2.100+...+99.100+100.100 - (1.2 +2.3+ 3.4+...+99.100)

Đặt B = 1.100 + 2.100+...+99.100 + 100.100

C = 1.2 + 2.3 + 3.4 +...+ 99.100

A = B - C

B = 1.100 + 2.100 + ...+ 99.100 + 100.100

B = 100.(1+ 2+ ... + 99+ 100)

B = 100.(100 + 1) x 100 : 2

B = 505000

C = 1.2 + 2.3 + 3.4 +...+ 99.100

3C = 1.2.3 + 2.3.3 +..+99.100.3

1.2.3 = 1.2.3

2.3.3 = 2.3.(4 - 1) = 2.3.4 - 1.2.3

99.100.3 = 99.100.(101 - 98)=99.100.101-98.99.100

Cộng vế với vế ta có:

3C = 99.100.101

C = 99.100.101 : 3

C = 333300

A = B - C

A = 505000 - 333300

A = 171700

Câu b:

A = 9+99+ 999+...+9999...99(1000 chữ số 9)

9 = - 1 + 10

99 = - 1 + 100

999 = - 1 + 1000

...............................

999...999 = -1 + 1000...00(1000 chữ số 0)

Cộng vế với vế ta có:

B = - 1 x 1000 + 11111...10(1000 chữ số 1)

B = 111....110110 (999 chữ số 1)

Ta có: D\(=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2005}\right)\)

\(\Leftrightarrow D=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{2004}{2005}=\dfrac{1.2.3...2004}{2.3.4...2005}=\dfrac{1}{2005}\)

Ta có: \(E=\dfrac{1^2}{1.3}.\dfrac{2^2}{2.4}.\dfrac{3^2}{3.5}...\dfrac{999^2}{999.1000}.\dfrac{1000^2}{1000.1001}=\dfrac{\left(1.2.3.4...1000\right)\left(1.2.3.4...1000\right)}{\left(1.2.3....1000\right)\left(3.4.5....1001\right)}=\dfrac{2}{1001}\)

bn lm sai rồi