K
Khách

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

15 tháng 3 2018

\(A=\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1}{3^{2014}}\)

\(3A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{2013}}\)

\(3A-A=\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{2013}}\right)-\left(\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1}{3^{2014}}\right)\)

\(2A=\frac{1}{3}-\frac{1}{3^{2014}}\)

\(A=\frac{\frac{1}{3}-\frac{1}{3^{2014}}}{2}\)

11 tháng 5 2015

Bạn nên nhớ các bài dạng dãy số này, sau này sẽ cần dùng rất nhiều:

 Ta có:  \(A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2014}}\)

          \(2A=2\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2014}}\right)\)

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

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

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

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

11 tháng 5 2015

Ta có:\(A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2014}}\)

\(\Rightarrow2A=2+1+\frac{1}{2}+...+\frac{1}{2^{2013}}\)

\(\Leftrightarrow2A-A=\left(2+1+\frac{1}{2}+...+\frac{1}{2^{2013}}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2^{2014}}\right)\)

\(=2-\frac{1}{2^{2014}}=\frac{2^{2015}-1}{2^{2014}}\)

Vậy \(A=\frac{2^{2015}-1}{2^{2014}}\)

30 tháng 4 2018

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

\(\Rightarrow3A=3+1+\frac{1}{3}+...+\frac{1}{3^{2013}}\)

\(\Rightarrow3A-A\)=  \(\left(3+1+...+\frac{1}{3^{2013}}\right)-\left(1+\frac{1}{3}+...+\frac{1}{3^{2014}}\right)\)

\(\Rightarrow2A=3-\frac{1}{3^{2014}}\)

\(\Rightarrow A=\frac{3-\frac{1}{3^{2014}}}{2}\)

\(\Rightarrow A=\frac{3}{2}-\frac{\frac{1}{3^{2014}}}{2}< \frac{3}{2}\)

Vậy  \(A< \frac{3}{2}\)

Chúc bạn học tốt !!! 

13 tháng 8 2015

 ====== 83/88 

22 tháng 5 2017

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

\(\Rightarrow3A=1+\frac{1}{3}+\frac{1}{3^2}+....+\frac{1}{3^{2013}}\)

\(\Rightarrow3A-A=1-\frac{1}{3^{2014}}\)

\(\Rightarrow2A=1-\frac{1}{3^{2014}}\)

\(\Rightarrow A=\left(1-\frac{1}{3^{2014}}\right):2=\frac{1}{2}-\frac{1}{3^{2014}.2}=\frac{3^{2014}-1}{3^{2014}.2}\)

b.\(B=\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{2014}}\)

\(\Rightarrow2B=1+\frac{1}{2^2}+....+\frac{1}{2^{2013}}\)

\(\Rightarrow2B-B=1-\frac{1}{2^{2014}}\)

\(\Rightarrow B=1-\frac{1}{2^{2014}}\)

8 tháng 5 2018

\(A=\frac{\frac{2017}{1}+\frac{2016}{2}+\frac{2015}{3}+...+\frac{1}{2017}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2018}}\)

\(A=\frac{1+\left(1+\frac{2016}{2}\right)+\left(1+\frac{2015}{3}\right)+...+\left(1+\frac{1}{2017}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2018}}\)

\(A=\frac{\frac{2018}{2018}+\frac{2018}{2}+\frac{2018}{3}+...+\frac{2018}{2017}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2018}}\)

\(A=\frac{2018\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2017}+\frac{1}{2018}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2018}}\)

\(A=2018\)

8 tháng 5 2018

Ta có : 

\(A=\frac{\frac{2017}{1}+\frac{2016}{2}+\frac{2015}{3}+...+\frac{1}{2017}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}}\)

\(A=\frac{\left(\frac{2017}{1}-1-1-...-1\right)+\left(\frac{2016}{2}+1\right)+\left(\frac{2015}{3}+1\right)+...+\left(\frac{1}{2017}+1\right)}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}}\)

\(A=\frac{\frac{2018}{2018}+\frac{2018}{2}+\frac{2018}{3}+...+\frac{2018}{2017}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}}\)

\(A=\frac{2018\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}\right)}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}}\)

\(A=2018\)

Vậy \(A=2018\)

Chúc bạn học tốt ~ 

25 tháng 6 2016

A =\(\frac{1}{1+2}\)+\(\frac{1}{1+2+3}\)+...+\(\frac{1}{1+2+3+4...+2014}\)

\(\Rightarrow A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{2029105}\)

\(\Rightarrow2A=2\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{2029105}\right)\)

\(\Rightarrow2A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{4058210}\)

\(\Rightarrow2A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2014.2015}\)

\(\Rightarrow2A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2014}-\frac{1}{2015}\)

\(\Rightarrow2A=\frac{1}{2}-\frac{1}{2015}\)

\(\Rightarrow2A=\frac{2013}{4030}\)

\(\Rightarrow A=\frac{2013}{8060}\)

1 tháng 7 2016

ngài Kiệt ღ ๖ۣۜLý๖ۣۜ   đúng là không ái sánh bằng sự gian xảo này

25 tháng 5 2016

\(2A=2\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\right)\)

\(2A=2+1+...+\frac{1}{2^{2011}}\)

\(2A-A=\left(2+1+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+...+\frac{1}{2^{2010}}\right)\)

\(A=2-\frac{1}{2^{2012}}\)

26 tháng 2 2017

A=\(1\frac{1}{2}.1\frac{1}{3}.1\frac{1}{4}....1\frac{1}{2015}\)

A=\(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}....\frac{2016}{2015}\)

A=\(\frac{3.4.5.....2016}{2.3.4....2015}\)

A=\(\frac{2016}{2}=1008\)

26 tháng 2 2017

nhanh tay lên các bạn ai trả lời đầu tiên mình cho 5 cái tick