tính
A = \(\frac{2}{60.63}\)+ \(\frac{2}{63.66}\)+ \(\frac{2}{66.69}\)+ ...+ \(\frac{2}{117.120}\)+ \(\frac{2}{2011}\)
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
LN
0
A
1
31 tháng 3 2015
TÍNH A SẼ BÍT
TA CÓ:A=2/3x3/60x63+2/3x3/63x66+2/3x3/66x69+.....+2/3x3/117x120
A=2/3x(3/60x63+3/63x66+3/66x69+.....+3/117x120
A=2/3x(3/60-3/63+3/63-3/66+3/66-3/69+....+3/117-3/120)
A=2/3x(3/60-3/120)
A=2/3x1/40
A=2/120=1/60
1/60 VA 2/2011
1/60 >2/2011
21 tháng 7 2018
C=1/2.(3/60.63+....+3/117.120)+1/1003
C=1/2.(1/60-1/63+....+1/117-1/120)+1/1003
....còn lại tự làm nha, bài còn lại cũng tương tự
Y
21 tháng 7 2018
Ta có:
\(C=\dfrac{2}{60.63}+\dfrac{2}{63.66}+...+\dfrac{2}{117.120}+\dfrac{2}{2006}\)
\(C=2\left(\dfrac{1}{60.63}+\dfrac{1}{63.66}+...+\dfrac{1}{117.120}\right)+\dfrac{2}{2006}\)
\(C=2.\dfrac{1}{3}\left(\dfrac{3}{60.63}+\dfrac{3}{63.66}+...+\dfrac{3}{117.120}\right)+\dfrac{2}{2006}\)
\(C=\dfrac{2}{3}\left(\dfrac{1}{60}-\dfrac{1}{63}+\dfrac{1}{63}-\dfrac{1}{66}+...+\dfrac{1}{117}-\dfrac{1}{120}\right)+\dfrac{2}{2006}\)
\(C=\dfrac{2}{3}\left(\dfrac{1}{60}-\dfrac{1}{120}\right)+\dfrac{2}{2006}\)
\(C=\dfrac{2}{3}.\dfrac{1}{120}+\dfrac{2}{2006}\)
\(C=\dfrac{1}{180}+\dfrac{2}{2006}\)
Ta lại có:
\(D=\dfrac{5}{40.44}+\dfrac{5}{44.48}+...+\dfrac{5}{76.80}+\dfrac{5}{2006}\)
\(D=5\left(\dfrac{1}{40.44}+\dfrac{1}{44.48}+...+\dfrac{1}{76.80}\right)+\dfrac{5}{2006}\)
\(D=5.\dfrac{1}{4}\left(\dfrac{4}{40.44}+\dfrac{4}{44.48}+...+\dfrac{4}{76.80}\right)+\dfrac{5}{2006}\)
\(D=\dfrac{5}{4}\left(\dfrac{1}{40}-\dfrac{1}{44}+\dfrac{1}{44}-\dfrac{1}{48}+...+\dfrac{1}{76}-\dfrac{1}{80}\right)+\dfrac{5}{2006}\)
\(D=\dfrac{5}{4}\left(\dfrac{1}{40}-\dfrac{1}{80}\right)+\dfrac{5}{2006}\)
\(D=\dfrac{5}{4}.\dfrac{1}{80}+\dfrac{5}{2006}\)
\(D=\dfrac{1}{64}+\dfrac{5}{2006}\)
Vì \(\dfrac{1}{180}< \dfrac{1}{64}\)
\(\dfrac{2}{2006}< \dfrac{5}{2006}\)
\(\Rightarrow\dfrac{1}{180}+\dfrac{2}{2006}< \dfrac{1}{64}+\dfrac{5}{2006}\)
\(\Rightarrow C< D\)
BH
21 tháng 7 2018
dở ẹt nhu cu net ma ko biet lamb tao hoc lop mau giao tao cung biet tra loi dung la ngu
F
20 tháng 4 2019
\(A=\frac{2}{60\cdot63}+\frac{2}{63\cdot66}+...+\frac{2}{117\cdot120}+\frac{2}{2003}\)
\(\text{Đặt }C=\frac{2}{60\cdot63}+\frac{2}{63\cdot66}+...+\frac{2}{117\cdot120}\)
\(C=\frac{2}{3}\left(\frac{3}{60\cdot63}+\frac{3}{63\cdot66}+...+\frac{3}{117\cdot120}\right)\)
\(C=\frac{2}{3}\left(\frac{1}{60}-\frac{1}{63}+\frac{1}{63}-\frac{1}{66}+...+\frac{1}{117}-\frac{1}{120}\right)\)
\(C=\frac{2}{3}\left(\frac{1}{60}-\frac{1}{120}\right)\)
\(C=\frac{2}{3}\cdot\frac{1}{120}\)
\(C=\frac{1}{180}\)
\(\text{Thay }C=\frac{1}{180}\text{Ta có : }\) \(A=\frac{1}{180}+\frac{2}{2003}\)
\(B=\frac{5}{40\cdot44}+\frac{5}{44\cdot48}+...+\frac{5}{76\cdot80}+\frac{5}{2003}\)
\(\text{Đặt }D=\frac{5}{40\cdot44}+\frac{5}{44\cdot48}+...+\frac{5}{76\cdot80}\)
\(D=\frac{5}{4}\left(\frac{4}{40\cdot44}+\frac{4}{44\cdot48}+...+\frac{4}{76\cdot80}\right)\)
\(D=\frac{5}{4}\left(\frac{1}{40}-\frac{1}{44}+\frac{1}{44}-\frac{1}{48}+...+\frac{1}{76}-\frac{1}{80}\right)\)
\(D=\frac{5}{4}\left(\frac{1}{40}-\frac{1}{80}\right)\)
\(D=\frac{5}{4}\cdot\frac{1}{80}\)
\(D=\frac{1}{64}\)
\(\text{Thay }D=\frac{1}{64}\text{ Ta có : }B=\frac{1}{64}+\frac{5}{2003}\)
\(\text{Vì }A=\frac{1}{180}+\frac{2}{2003}\text{ , }B=\frac{1}{64}+\frac{5}{2003}\)
\(\text{Có : }\frac{1}{180}< \frac{1}{64}\)
\(\frac{2}{2003}< \frac{5}{2003}\)
\(\Rightarrow\text{ }A< B\)
Để mình làm lại nguyên bài cho dễ hiểu nhé
\(A=\frac{2}{60.63}+\frac{2}{63.66}+\frac{2}{66.69}+..+\frac{2}{117.120}+\frac{2}{2011}\)
\(=\frac{2}{3}\left(\frac{2}{60}-\frac{2}{63}+\frac{2}{63}-\frac{2}{66}+\frac{2}{66}-\frac{2}{69}+...+\frac{2}{117}-\frac{2}{120}\right)+\frac{2}{2011}\)
\(=\frac{2}{3}\left(\frac{2}{60}-\frac{2}{120}\right)+\frac{2}{2011}=\frac{2}{3}.\frac{1}{60}+\frac{2}{2011}=\frac{4382}{361980}\)
Sorry nhé! nãy giờ nhìn không kĩ đề
\(A=\frac{2}{60.63}+\frac{2}{63.66}+\frac{2}{66.69}+...+\frac{2}{117.120}\)
\(=\frac{2}{3}\left(\frac{2}{60}-\frac{2}{63}+\frac{2}{63}-\frac{2}{66}+\frac{2}{66}-\frac{2}{69}+...+\frac{2}{117}-\frac{2}{120}\right)\)
\(=\frac{2}{3}\left(\frac{2}{60}-\frac{2}{120}\right)=\frac{2}{3}.\frac{1}{60}=\frac{2}{180}\)
Suy ra \(A=\frac{2}{180}\)