mik chịu mà bn thức khuya để học bài à ?? bn chăm thế !!

bạn có ranh không vậy 

2 = 1 + 1     6 = 2 + 4     8 = 5 + 3     10 = 8 + 2

3 = 1 + 2     6 = 3 + 3     8 = 4 + 4     10 = 7 + 3

4 = 3 + 1     7 = 1 + 6     9 = 8 + 1     10 = 6 + 4

4 = 2 + 2     7 = 5 + 2     9 = 6+ 3     10 = 5 + 5

5 = 4 + 1     7 = 4 + 3     9 = 7 + 2     10 = 10 + 0

5 = 3 + 2     8 = 7 + 1     9 = 5 + 4     10 = 0 + 10

6 = 5 + 1     8 = 6 + 2     10 = 9 + 1     1 = 1 + 0

Tiếng  việt  khó .

NHẢM NHÍ

ai chat nhìu thì kt bn với mình nha

-27 nhá bạn

27 là dung

Kq = 27

154

báo cáo

154

Giải:

a) Gọi dãy đó là A, ta có:

\(A=\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2014}}\) 

\(2A=\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2013}}\) 

\(2A-A=\left(\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2013}}\right)-\left(\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2014}}\right)\) 

\(A=\dfrac{1}{2}-\dfrac{1}{2^{2014}}\) 

Vì \(\dfrac{1}{2}< 1;\dfrac{1}{2^{2014}}< 1\) nên \(\dfrac{1}{2}-\dfrac{1}{2^{2014}}< 1\) 

\(\Rightarrow A< 1\) 

b) \(A=\dfrac{10^{11}-1}{10^{12}-1}\) và \(B=\dfrac{10^{10}+1}{10^{11}+1}\) 

Ta có:

\(A=\dfrac{10^{11}-1}{10^{12}-1}\) 

\(10A=\dfrac{10^{12}-10}{10^{12}-1}\) 

\(10A=\dfrac{10^{12}-1+9}{10^{12}-1}\) 

\(10A=1+\dfrac{9}{10^{12}-1}\) 

Tương tự:

\(B=\dfrac{10^{10}+1}{10^{11}+1}\) 

\(10B=\dfrac{10^{11}+10}{10^{11}+1}\) 

\(10B=\dfrac{10^{11}+1+9}{10^{11}+1}\) 

\(10B=1+\dfrac{9}{10^{11}+1}\) 

Vì \(\dfrac{9}{10^{12}-1}< \dfrac{9}{10^{11}+1}\) nên \(10A< 10B\) 

\(\Rightarrow A< B\)

Kết quả HÌNH NHƯ =1 đó bn

kết quả HÌNH NHƯ =1 đó bn

\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(A=\left(1+\frac{1}{3}+...+\frac{1}{9}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\)

\(A=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{9}+\frac{1}{10}\right)-2.\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\)

\(A=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{9}+\frac{1}{10}\right)-\left(1+\frac{1}{2}+...+\frac{1}{5}\right)\)

\(A=\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+...+\frac{1}{10}\)

\(B=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)-2.\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\)

\(B=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{5}\right)\)

Vậy A = B và A = 1/6 + 1/7 + 1/8 + 1/9 + 1/10

1/ A= \(\left(\frac{1}{1.2}\right)+\left(\frac{1}{3.4}\right)+...+\left(\frac{1}{9.10}\right)\)

B=(1/1+1/2+1/3+...+1/10)- (1/1+1/2+...+1/5)

<=> B=1/6+1/7+1/8+1/9+1/10.

\(\left(1-\dfrac{1}{10}\right):\left(1+\dfrac{1}{10}\right):\left(1+\dfrac{1}{11}\right):\left(1+\dfrac{1}{12}\right):...:\left(1+\dfrac{1}{500}\right)\)

=\(\dfrac{9}{10}:\dfrac{11}{10}:\dfrac{12}{11}:\dfrac{13}{12}:...:\dfrac{501}{500}\)

=\(\dfrac{9}{10}.\dfrac{10}{11}:\dfrac{12}{11}:\dfrac{13}{12}:...:\dfrac{501}{500}\)

=\(\dfrac{9}{11}:\dfrac{12}{11}:\dfrac{13}{12}:...:\dfrac{501}{500}\)=\(\dfrac{9}{501}\)=\(\dfrac{3}{167}\)