chứng minh A>B
A= 2/5.7 + 5/7.12 + 7/12.19 + 9/19.28 + 11/28.39 + 1/30.40
B= 1/20 + 1/44 + 1/77 + 1/119 + 1/170
Chứng minh A > B, biết:
A=2/5.7+5/7.12+7/12.19+9/19.28+11/28.39+1/30.40
B=1/20+1/44+1/77+1/119+1/170
Ta có : +) A= 1/5 -1/7 +1/7 -1/12 +1/12 - 1/19 +1/19 - 1/28 +1/28 - 1/39 +1/30.40 ⇔ A=1/5 -1/39 +1/30.40
+) B= 2.(1/5.8 +1/8.11 +1/11.14 +1/14.17 + 1/17.20 )
⇔B=2. 1/3.(1/5 - 1/8 +1/8 - 1/11 +1/11- 1/14 +1/14 -1/17 +1/17 -1/20 )
⇔B=2/3.( 1/5-1/20 ) Ta luôn có :B luôn <1/5 - 1/20
Mà 1/5 -1/20 <1/5 -1/39 +1/30.40 =A
⇒ A>B (dpcm) Tích mình với nha bn .
Chứng minh A > B, biết:
A= \(\dfrac{2}{5.7}+\dfrac{5}{7.12}+\dfrac{7}{12.19}+\dfrac{9}{19.28}+\dfrac{11}{28.39}+\dfrac{1}{30.40}\)
B= \(\dfrac{1}{20}+\dfrac{1}{44}+\dfrac{1}{77}+\dfrac{1}{119}+\dfrac{1}{170}\)
Giúp mình với mình đang cần gấp!!!
Đây nha bạn:
=7−55.7+12−77.12+19−1212.19+28−1919.28+39−2828.39+40−3939.40
=15−17+17−112+112−119+119−128+128−139+139−140
=15−140=740
Tính tỉ số A/B biết:
A = 2/5.7 + 5/7.12 + 7/12.19 + 9/19.28 + 11/28.39 + 1/39.40
B = 1/20 + 1/44 + 1/77 +1/119 + 1/170
\(A=\frac{2}{5.7}+\frac{5}{7.12}+\frac{7}{12.19}+\frac{9}{19.28}+\frac{11}{28.39}+\frac{1}{39.40}\)
\(=\frac{7-5}{5.7}+\frac{12-7}{7.12}+\frac{19-12}{12.19}+\frac{28-19}{19.28}+\frac{39-28}{28.39}+\frac{40-39}{39.40}\)
\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{19}+\frac{1}{19}-\frac{1}{28}+\frac{1}{28}-\frac{1}{39}+\frac{1}{39}-\frac{1}{40}\)
\(=\frac{1}{5}-\frac{1}{40}=\frac{7}{40}\)
\(B=\frac{1}{20}+\frac{1}{44}+\frac{1}{77}+\frac{1}{119}+\frac{1}{170}\)
\(=\frac{2}{40}+\frac{2}{88}+\frac{2}{154}+\frac{2}{238}+\frac{2}{340}\)
\(=\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}+\frac{2}{17.20}\)
\(=\frac{2}{3}\left(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}\right)\)
\(=\frac{2}{3}\left(\frac{8-5}{5.8}+\frac{11-8}{8.11}+\frac{14-11}{11.14}+\frac{17-14}{14.17}+\frac{20-17}{17.20}\right)\)
\(=\frac{2}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\right)\)
\(=\frac{2}{3}\left(\frac{1}{5}-\frac{1}{20}\right)=\frac{1}{10}\)
\(\frac{A}{B}=\frac{\frac{7}{40}}{\frac{1}{10}}=\frac{7}{4}\)
Chứng minh A > B, biết A = \(\dfrac{2}{5.7}+\dfrac{5}{7.12}+\dfrac{7}{12.19}+\dfrac{9}{19.28}+\dfrac{11}{28.39}+\dfrac{1}{39.40}\)
B = \(\dfrac{1}{20}+\dfrac{1}{44}+\dfrac{1}{77}+\dfrac{1}{119}+\dfrac{1}{170}\)
ta tách 2/5x7 = 2/5-2/7 tách những cái kia tương tự góp vào rồi tính
Tính tỉ số A và B, biết: A= 2/5.7 + 5/7.12 + 7/12.19 + 9/19.28 + 11/28.39 + 1/39.40
B= 1/20 + 1/44 + 1/77 + 1/119 + 1/170
Bài 2...: Chứng minh A >B, biết:
A=2/5x7 + 5/7x12 + 7/12x19 + 9/19x28 + 11/28x39 + 1/30x40
B=1/20 + 1/44 + 1/77 + 1/119 + 1/170
Sửa đề: 39*40
\(A=\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{12}+...+\dfrac{1}{39}-\dfrac{1}{40}=\dfrac{1}{5}-\dfrac{1}{40}=\dfrac{7}{40}\)
\(B=\dfrac{2}{3}\left(\dfrac{1}{5\cdot8}+\dfrac{1}{8\cdot11}+...+\dfrac{1}{17\cdot20}\right)\)
\(=\dfrac{2}{3}\left(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{17}-\dfrac{1}{20}\right)\)
=2/3*3/20=2/20=1/10=4/40<A
So sánh 10^2000+5/10^2001-8 và 10^2000+6/10^2001-7
Tính 1+13^4+13^8+...+13^96+13^100/1+13^2+13^4+...+13^98+13^100+13^102
Tính A=2/5.7+5/7.12+9/19.28+11/28.39+1/39.40
1/5+1/20+1/44+1/77+1/119+1/170
Tính tổng :
a) B = \(\dfrac{1}{5}\) + \(\dfrac{1}{20}\)+ \(\dfrac{1}{44}\) +\(\dfrac{1}{77}\) +\(\dfrac{1}{119}\) + \(\dfrac{1}{170}\) +\(\dfrac{1}{230}\) +\(\dfrac{1}{299}\)
b) C = \(\left(1+\dfrac{1}{1.3}\right)\) \(\left(1+\dfrac{1}{2.4}\right)\) \(\left(1+\dfrac{1}{3.5}\right)\) .....\(\left(1+\dfrac{1}{2014.2016}\right)\)
Câu C giải rồi
\(B=\dfrac{1}{5}+\dfrac{1}{20}+\dfrac{1}{44}+\dfrac{1}{77}+\dfrac{1}{119}+\dfrac{1}{170}+\dfrac{1}{230}+\dfrac{1}{299}\)
\(=2\left(\dfrac{1}{10}+\dfrac{1}{40}+\dfrac{1}{88}+\dfrac{1}{154}+\dfrac{1}{238}+\dfrac{1}{340}+\dfrac{1}{460}+\dfrac{1}{598}\right)\)
\(=\dfrac{2}{3}\left(\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+\dfrac{3}{11.14}+\dfrac{3}{14.17}+\dfrac{3}{17.20}+\dfrac{3}{20.23}+\dfrac{3}{23.26}\right)\)
\(=\dfrac{2}{3}\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+...+\dfrac{1}{23}-\dfrac{1}{26}\right)\)
\(=\dfrac{2}{3}\left(\dfrac{1}{2}-\dfrac{1}{26}\right)=\dfrac{4}{13}\)