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\(A=\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+....+\frac{1}{496}-\frac{1}{501}\right):5\)
\(A=\left(1-\frac{1}{501}\right):5\)
\(A=\frac{500}{501}:5=\frac{100}{501}\)
Ta có : \(A=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.501}\)
\(\Rightarrow\) \(A=\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{496}-\frac{1}{501}\right) \)
\(\Rightarrow\) \(A=\frac{1}{5}\left(1-\frac{1}{501}\right)\)
\(\Rightarrow\) \(A=\frac{1}{5}.\frac{501-1}{501}=\frac{1}{5}.\frac{500}{501}\)
\(\Rightarrow\) \(A=\frac{1.500}{5.501}=\frac{20}{1.501}=\frac{20}{501}\)
Vậy \(A=\frac{20}{501}\)
B = 1/1.6 + 1/6.11 + 1/11.16 + ... + 1/496.501
B x 5 = 5/1.6 + 5/6.11 + 5/11.16 + ... + 5/496.501
B x 5 = 1 - 1/6 + 1/6 - 1/11 + 1/11 - 1/16 + ... + 1/496 - 1/501
B x 5 = 1 - 1/501
B x 5 = 500/501
B = 500/501 : 5
B = 100/501
\(B=\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{9.10}\)
\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....++\frac{1}{9}-\frac{1}{10}\)
\(B=1-\frac{1}{10}=\frac{9}{10}\)
\(C=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)
\(C=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(C=1-\frac{1}{100}\)
\(C=\frac{99}{100}\)
đặt 5 ra ngoài
A=5.(5/1.6+5/6.11+...+5/2016.2021)
= 5.(1/1-1/6+1/6-1/11+....+1/2016-1/2021)
=5.(1/1-1/2021)
=5.2020/2021
tính nốt
A=5^2/1.6+5^2/6.11+5^2/11.16+...+5^2/2016.2021
=5(5/1.6+5/6.11+5/11.16+...+5/2016.2021)
=5(1-1/2021)
=5.2020/2021
=10100/2021
tick nha ^^
\(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{46.51}\)
\(=\frac{1}{5}.\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{46.51}\right)\)
\(=\frac{1}{5}.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{46}-\frac{1}{51}\right)\)
\(=\frac{1}{5}.\left(1-\frac{1}{51}\right)\)
\(=\frac{1}{5}.\left(\frac{51}{51}-\frac{1}{51}\right)\)
\(=\frac{1}{5}.\frac{50}{51}\)
\(=\frac{10}{51}\)
Chúc bạn học tốt !!!
\(A=\)\(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{51.56}\)
\(5A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{51.56}\)
\(5A=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{51}-\frac{1}{56}\)
\(5A=1-\frac{1}{56}=\frac{55}{56}\)
\(A=\frac{55}{56}\div5=\frac{55}{56}.\frac{1}{5}=\frac{11}{56}\)
(1/2 +1) . (1/3+1). ( 1/4+1). ..... . (1/99+1)
= 3/2 . 4/3 . 5/4 . ....... . 100/ 99
= 3.4.5.....100 / 2.3.4......99
= 100/2 =50
ai t ick mk mk t ick lại
Nhân A với 5 ta được
A .5=5.(1/1.6 +1/6.11+1/11.16+....+1/496.561)
A .5=5/1.6+5/6.11+5/11.16+...+5/496.561
A .5=1-1/6+1/6-1/11+1/11-1/16+...+1/496-1/561
A .5=1-1/561
A .5=560/561
A =560/561 : 5 =112/561
\(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.561}\)
\(=\left(\frac{1}{1}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{11}\right)+\left(\frac{1}{11}-\frac{1}{16}\right)+...+\left(\frac{1}{496}-\frac{1}{561}\right)\)
\(=\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{496}-\frac{1}{561}\)
\(=\frac{1}{1}-\frac{1}{561}\)
\(=\frac{561}{561}-\frac{1}{561}\)
\(=\frac{560}{561}\)
\(\Rightarrow\) Vậy, \(A=\frac{560}{561}\)
Giải
= 1/5 . ( 1 - 1/6 + 1/6 - 1/11 + . ... + 1/496 - 1/501)
= 1/5 . ( 1-1/501)
= 1/5 . 500/501
= 100/501
Bạn nhân trên tử vào 6 tất cả các phân số! Rồi tách ra là làm đc thui!