\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{99.100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}\)

\(=\frac{99}{100}\)

Dấu chấm là nhân

a) \(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{99.100}\) \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}=\frac{99}{100}\)

b) \(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{97.99}\) \(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{97}-\frac{1}{99}=1-\frac{1}{99}=\frac{98}{99}\)

c) Đặt \(C=\frac{4}{5.7}+\frac{4}{7.9}+....+\frac{4}{59.61}\)

\(\Rightarrow\frac{1}{2}C=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+....+\frac{1}{59}-\frac{1}{61}\)

\(\Rightarrow\frac{1}{2}C=\frac{1}{5}-\frac{1}{61}=\frac{56}{305}\)

\(\Rightarrow C=\frac{56}{305}:\frac{1}{2}=\frac{112}{305}\)

CHÚC BẠN HỌC TỐT NHA! ĐÚNG THÌ NHA!

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{97.99}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{97}-\frac{1}{99}\)

\(=1-\frac{1}{99}\)

\(=\frac{98}{99}\)

help mik với

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{98}-\dfrac{1}{99}\)

\(=1-\dfrac{1}{99}=\dfrac{98}{99}\)

\(=\dfrac{1}{3}\times\dfrac{3}{5}\times...\times\dfrac{97}{99}\)

\(=\dfrac{1\times3\times...\times97}{3\times5\times...\times99}=\dfrac{1}{99}\)

a) 1 + 1/4 + 1/8 + 1/16

= 16/16 + 4/16 + 2/16 + 1/16

= 23/16

b) 2 - 1/8 - 1/12 - 1/16

= 96/48 - 6/46 - 4/48 - 3/48

= 83/48

c) 4/99 × 18/5 : 12/11 + 3/5

= 8/55 : 12/11 + 3/5

= 2/15 + 3/5

= 2/15 + 9/15

= 11/15

d) (1 - 3/4) × (1 + 1/3) : (1 - 1/3)

= 1/4 × 4/3 : 2/3

= 1/3 : 2/3

= 2

1 + 1/4 + 1/8 + 1/16

= 16 + 4 + 2 + 1 / 16

=23/16

2-1/8-1/12-1/16

= 96 - 6 - 4 - 3 / 48

= 83 / 48

4/99 x 18/5 : 12 /11 + 3/5

= 4/99 x 18/5 x 11/12 + 3/5

= 2/15 + 3/5

= 11/15

(1 - 3/4) x (1+1/3) : (1-1/3) 

= 1/4 x 4/3 : 2/3

= 1/4 x 4/3 x 3/2

= 1/2

A = 2/3 . 3/4 . 4/5 ..... 98/99

A = 2 . 3 . 4 ....... 98/3 . 4 . 5 ...... 99

A = 2/99

A=(1-1/3)x(1-1/4)...x(1-1/99)

  =2/3x3/4x4/5x...x98/99

a)

Ta có : ( 1 + 2 + 3 + ... + 99)

Số số hạng là:       ( 99 - 1 )  : 1 + 1 = 100

Tổng là:                 ( 99 + 1 ) x 100 : 2 = 5000

=> 5000 x ( 13  - 12 - 1 ) x 15

=> 5000 x 10 x 15

=> 50000 x 15

=> 750000

Ko muốn vt nx :))

2/99 nha bạn mình làm rồi

ở violympic đúng ko

\(\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot\left(1-\frac{1}{5}\right)\cdot...\cdot\left(1-\frac{1}{99}\right)\)

\(=\frac{2}{3^{\left(1\right)}}\cdot\frac{3^{\left(1\right)}}{4^{\left(1\right)}}\cdot\frac{4^{\left(1\right)}}{5^{\left(1\right)}}\cdot...\cdot\frac{98^{\left(1\right)}}{99}\)

\(=\frac{2}{99}\)

a) (4/5+3/10+1/5+7/10) x 3 x 5/6 bằng (1+1) x 3 x 5/6 bằng 6x 5/6 bằng 5 

b) đặt 1+3+5+...+99 là A suy ra A x(2-2) bằng A x0 bằng 0

dấu bằng của mk bị liệt r nên bạn chịu khó đọc nha

a [(4/5+1/5)+(3/10+7/10)]*5/2                    b (1+3+5+................+99)*(2-2)

=(1+1)*5/2                                                =(1+3+5+...............+99)*0

=5                                                           =0