\(S=\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+\frac{3}{4.5}+....+\frac{3}{2015.2016}\)

\(\Rightarrow\frac{1}{3}.S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{2015.2016}\)

\(\Rightarrow\frac{1}{3}.S=\left(\frac{1}{1}-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+......+\left(\frac{1}{2015}-\frac{1}{2016}\right)\)

\(\Rightarrow\frac{1}{3}.S=\frac{1}{1}-\frac{1}{2016}\)

\(\Rightarrow\frac{1}{3}.S=\frac{2015}{2016}\)

\(\Rightarrow S=\frac{2015}{672}\)

Vậy: \(\Rightarrow S=\frac{2015}{672}\)

Bạn giải giúp mk câu mk đăng tầm 5 phút nha!

đơn giản

S=1/1-1/2+1/2-1/3+1/3-1/4+1\5-..............................-1/2015+1/2016

S=1/1-1/2016

S=2015/2016

sai bét

dễ lắm

s=

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

kb đi 

Ta có:

\(S=\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+.......+\frac{3}{2015.2016}\)

\(\Rightarrow\frac{1}{3}.S=\frac{1}{1.2}+\frac{1}{2.3}+......+\frac{1}{2015.2016}\)

\(\Rightarrow\frac{1}{3}.S=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+......+\left(\frac{1}{2015}-\frac{1}{2016}\right)\)

\(\Rightarrow\frac{1}{3}.S=1-\frac{1}{2016}=\frac{2015}{2016}\)

\(\Rightarrow S=\frac{2015}{672}\)

Vậy: S = 2015/672

\(A=\frac{1\cdot1}{1\cdot2}\cdot\frac{2\cdot2}{2\cdot3}\cdot\frac{3\cdot3}{3\cdot4}\cdot\frac{4\cdot4}{4\cdot5}=\frac{1\cdot2\cdot3\cdot4}{1\cdot2\cdot3\cdot4}\cdot\frac{1\cdot2\cdot3\cdot4}{2\cdot3\cdot4\cdot5}=\frac{1}{5}\)

A= 1/2 * 2/3 * 3/4 * 4/5

  =  1*2*3*4/2*3*4*5

  =   1/5

A = \(\frac{1\cdot1\cdot2\cdot2\cdot3\cdot3\cdot4\cdot4}{1\cdot2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot5}\)= \(\frac{\left(1\cdot2\cdot3\cdot4\right)\cdot\left(1\cdot2\cdot3\cdot4\right)}{\left(1\cdot2\cdot3\cdot4\right)\cdot\left(2\cdot3\cdot4\cdot5\right)}\)= \(\frac{1}{5}\)

Bạn k cho mik nhé.

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{2016.2017}\)

\(A=\left(\frac{1}{1}-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+......+\left(\frac{1}{2016}-\frac{1}{2017}\right)\)

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{2016}-\frac{1}{2017}\)

\(A=\frac{1}{1}-\frac{1}{2017}\)

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

A=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{2016.2017}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{2016}-\frac{1}{2017}\)

\(\Rightarrow A=1-\frac{1}{2017}\)

\(\Rightarrow A=\frac{2016}{2017}\)

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2015.2016}+\frac{1}{2016.2017}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2015}-\frac{1}{2016}+\frac{1}{2016}-\frac{1}{2017}\)

\(\Rightarrow A=1-\frac{1}{2017}\)

\(\Rightarrow A=\frac{2016}{2017}\)

\(1+\frac{1}{1+2}+\frac{1}{1+2+3}+....+\frac{1}{1+2+3+...+2015}\)

\(=\frac{2}{1.2}+\frac{1}{\frac{\left(1+2\right).2}{2}}+\frac{1}{\frac{\left(1+2+3\right).3}{2}}+.....+\frac{1}{\frac{\left(2015+1\right).2015}{2}}\)

\(=\frac{2}{1.2}+\frac{2}{2.3}+....+\frac{2}{2015.2016}\)

dễ vãi cả đạn

Thanks bạn nhiều tại câu này mk ko tk đúng đc cho bn nên mk tk đúng cho bn ở câu tl khác rồi nha

Chúc bn học tốt

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2016\cdot2017}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2016}-\frac{1}{2017}\)

\(=1-\frac{1}{2017}=\frac{2016}{2017}\)

a) = 2(1-1/2+1/2-1/3+...+1/19-1/20)

    = 2(1-1/20)

    = 2.19/20

    = 19/10

b) = 7(1/2-1/3+1/3-1/4+...+1/6-1/7)

   = 7(1/2 - 1/7)

   = 7.5/14

   = 5/2

c) = 1/2-1/5+1/5-1/8+...+1/14-1/17

   = 1/2 - 1/17

   = 15/34

Chúc bạn học tốt nhé

a)2/1.2+2/2.3+....+2/19.20

=2(1/1.2+1/2.3+....+1/19.20)

=2(1-1/2+1/2-1/3+.....-1/20)

=2(1-1/20)

2(19/20)=38/20=19/10

b)7/2.3+7/3.4+7/4.5+7/5.6+7/6.7

7(1/2.3+1/3.4+1/4.5+1/5.6+1/6.7)

7(1/2-1/3+1/3-1/4+.....-1/7)

7(1/2-1/7)

7(7/14-2/14)=7.5/14=35/14=5/2

c)3/2.5+3/5.8+3/8.11+3/11.14+3/14.17

1/2-1/5+1/5-1/8+......+1/14-1/17

1/2-1/17=17/34-2/34=15/34

Đây là toán lp 6 chứ bn

A = 2/1.2 + 2/2.3 + ...+2/19.20

Áp dụng công thức : n/n.(n+1)=(1/n)-(1/n+1)

Ta có : A= 1/1.2 + 1/2.3+...+1/19.20

           A= 1/1 - 1/2 + 1/2 - 1/3 + ...+ 1/19 - 1/20

           A= 1/1 - 1/20 

           A= 19/20

k cho mk nha bn

\(M=\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.\frac{4^2}{4.5}=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}=\frac{1}{5}\)

\(N=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{99.101}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\)

\(=\frac{1}{3}-\frac{1}{101}=\frac{98}{303}\)

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

N=1/2x(1/3-1/101)

N=1/2x98/101

N=49/101

nhầm 98/303 mới đúng

\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}=\frac{1}{5}\)

\(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.\frac{4^2}{4.5}=\frac{1^2.2^2.3^2.4^2}{1.2^2.3^2.4^2.5}=\frac{1}{5}\)