K
Khách

Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.

15 tháng 7 2019

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{153.155}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{153}-\frac{1}{155}\)

\(=1-\frac{1}{155}\)

\(=\frac{154}{155}\)

~Study well~

#JDW

15 tháng 7 2019

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+.......+\frac{2}{153.155}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.......+\frac{1}{153}-\frac{1}{155}\)

\(=1-\frac{1}{155}\)

\(=\frac{154}{155}\)

Bài 5:

a) Ta có: \(A=1\cdot2+2\cdot3+3\cdot4+...+9\cdot10\)

\(\Leftrightarrow3\cdot A=3\cdot\left(1\cdot2+2\cdot3+3\cdot4+...+9\cdot10\right)\)

\(\Leftrightarrow3A=1\cdot2\cdot\left(3-0\right)+2\cdot3\cdot\left(4-1\right)+3\cdot4\cdot\left(5-2\right)+...+9\cdot10\cdot\left(11-8\right)\)

\(\Leftrightarrow3A=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+3\cdot4\cdot5-2\cdot3\cdot4+...+8\cdot9\cdot10-8\cdot9\cdot10+9\cdot10\cdot11\)

\(\Leftrightarrow3\cdot A=9\cdot10\cdot11=90\cdot11=990\)

hay A=330

Vậy: A=330

16 tháng 5 2016

A=3/1*3+3/3*5+3/5*7+...+3/2015*2017

A=3/2*(2/1*3+2/3*5+2/5*7+...+2/2015*2017)

A=3/2*(1-1/3+1/3-1/5+1/5-1/7+...+1/2015-1/2017)

A=3/2*(1-1/2017)

A=3/2*2016/2017

A=3024/2017

16 tháng 5 2016

A= \(\frac{3}{1.3}\)+\(\frac{3}{3.5}\)+\(\frac{3}{5.7}\)+....+\(\frac{3}{2015.2017}\)

A= \(\frac{3}{2}\).(\(\frac{2}{1.3}\)+\(\frac{2}{3.5}\)+\(\frac{2}{5.7}\)+...+\(\frac{2}{2015.2017}\))

A= \(\frac{3}{2}\).( 1- \(\frac{1}{3}\)\(\frac{1}{3}\)\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{7}\)+... \(\frac{1}{2015}\)\(\frac{1}{2017}\))

A= \(\frac{3}{2}\).(1- \(\frac{1}{2017}\))

A= \(\frac{3}{2}\)\(\frac{2016}{2017}\)

A= \(\frac{3024}{2017}\)

23 tháng 3 2017

B=50/51 bạn ạ.

23 tháng 3 2017

50/51 bạn nhé

a) =1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101

    =1-1/101

    =100/101

b) =(2/1.3+2/3.5+2/5.7+...+2/99.101).2,5

    =(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101).2,5

    =(1-1/101).2,5

    =100/101.2,5

    =250/101

c) =(2/2.4+2/4.6+2/6.8+...+2/2008-2/2010).2

    =(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2008-1/2010).2

    =(1/2-1/2010).2

    =1004/1005

1 tháng 2 2015

[(2n+1)(2n+2)(2n+3)(2n+4):12]+(n+1)

DD
25 tháng 2 2021

\(A=1.3+3.5+5.7+...+\left(2n+1\right)\left(2n+3\right)\)

\(6A=1.3.\left(5+1\right)+3.5.\left(7-1\right)+5.7.\left(9-3\right)+...+\left(2n+1\right)\left(2n+3\right)\left(2n+5-2n+1\right)\)

\(6A=3+1.3.5-1.3.5+3.5.7-3.5.7+5.7.9-...-\left(2n-1\right)\left(2n+1\right)\left(2n+3\right)\)

\(+\left(2n+1\right)\left(2n+3\right)\left(2n+5\right)\)

\(6A=\left(2n+1\right)\left(2n+3\right)\left(2n+5\right)+3\)

\(A=\frac{\left(2n+1\right)\left(2n+3\right)\left(2n+5\right)+3}{6}\)

24 tháng 3 2017

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\)

\(=1-\frac{1}{51}=\frac{50}{51}\)

24 tháng 3 2017

2/1.3 + 2/3.5 + 2/5.7 + ... + 2/49 . 51

= 2/1.3 + 2/3.5 + 2/5.7 + ... + 2/49 . 51

= 1 + 51 = 52

28 tháng 4 2015

a)\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}=\left(1-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{7}\right)+...+\left(\frac{1}{99}-\frac{1}{101}\right)\)

                                                               \(=1-\frac{1}{101}=\frac{100}{101}\)

b) \(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{99.101}=\frac{2}{1.3}.\frac{5}{2}+\frac{2}{3.5}.\frac{5}{2}+\frac{2}{5.7}.\frac{5}{2}+...+\frac{2}{99.101}.\frac{5}{2}\)

                                                                \(=\frac{5}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)

                                                                \(=\frac{5}{2}.\frac{100}{101}=\frac{250}{101}\)

21 tháng 3 2016

a)100/101

b)250/101

14 tháng 4 2016

a.2/1.3+2/3.5+2/5.7+................+2/99.101

1-1/3+1/3-1/5+1/5-1/7+....+1/99-1/101

1-1/101

100/101

b.5/1.3+5/3.5+5/5.7+............+5/99.101

5.2/1.3.2+5.2/3.5.2+5.2/5.7.2+........+5.2+99.101.2

5/2(2/1.3+2/3.5+2/5.7+........+2/99.101)

5/2(1-1/3+1/3-1/5+1/5-1/7+........+1/99-1/101)

5/2(1-1/101)

5/2.100/101

250/101