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ta tách 2/5x7 = 2/5-2/7 tách những cái kia tương tự góp vào rồi tính
Đây nha bạn:
A=5.72+7.125+12.197+19.289+28.3911+39.401
=7−55.7+12−77.12+19−1212.19+28−1919.28+39−2828.39+40−3939.40=5.77−5+7.1212−7+12.1919−12+19.2828−19+28.3939−28+39.4040−39
=15−17+17−112+112−119+119−128+128−139+139−140=51−71+71−121+121−191+191−281+281−391+391−401
=15−140=740=
\(\frac{1}{5}+\frac{1}{20}+\frac{1}{44}+\frac{1}{77}+\frac{1}{119}+\frac{1}{170}+\frac{1}{230}+\frac{1}{299}\)
\(=\frac{1}{1.5}+\frac{1}{5.4}+\frac{1}{4.11}+\frac{1}{11.7}+...+\frac{1}{23.13}\)
\(=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{4}+...+\frac{1}{23}-\frac{1}{13}\)
\(=1-\frac{1}{13}\)
\(=\frac{12}{13}\)
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
\(\dfrac{1}{5}+\dfrac{1}{20}+\dfrac{1}{44}+\dfrac{1}{77}+\dfrac{1}{119}+\dfrac{1}{170}+\dfrac{1}{230}+\dfrac{1}{299}\)
=\(\dfrac{2}{10}+\dfrac{2}{40}+\dfrac{2}{88}+\dfrac{2}{154}+\dfrac{2}{238}+\dfrac{2}{340}+\dfrac{2}{460}+\dfrac{2}{598}\)
=\(\dfrac{1}{3}.2\left(\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+\dfrac{3}{11.14}+\dfrac{3}{14.17}+\dfrac{3}{17.20}+\dfrac{3}{20.23}+\dfrac{3}{23.26}\right)\)
=\(\dfrac{2}{3}\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{26}\right)\)
=\(\dfrac{2}{3}\left(\dfrac{1}{2}-\dfrac{1}{26}\right)\)
=\(\dfrac{2}{3}.\dfrac{6}{13}\)
=\(\dfrac{4}{13}\)
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 .