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5 tháng 3 2017
\(A=\frac{2}{3.5}+\frac{2}{5.7}+......+\frac{2}{99.100}\)
\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.....+\frac{1}{99}-\frac{1}{100}\)
\(A=\frac{1}{3}-\frac{1}{100}=\frac{97}{300}\)
ES
2
2 tháng 5 2018
Q = \(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2013.2015}\)
Q = \(\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{1}{2013.2015}\right)\)
Q = \(\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{2015}\right)\)
Q = \(\frac{1}{2}.\frac{2012}{6045}=\frac{1002}{6045}\)
2 tháng 5 2018
\(Q=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{2013.2015}\)
\(\Rightarrow Q.2=2.\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{2013.2015}\right)\)
\(\Rightarrow Q.2=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{2013.2015}\)
\(\Rightarrow Q.2=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2013}-\frac{1}{2015}\)
\(\Rightarrow Q.2=\frac{1}{3}-\frac{1}{2015}\)
\(\Rightarrow Q.2=\frac{2012}{6045}\)
\(\Rightarrow Q=\frac{2012}{6045}.\frac{1}{2}=\frac{1006}{6045}\)
Mk tinh nhẩm, nên ko bt kết quả có đúng ko
nên bn thử tính lại kết quả nha!!!
Chúc bn hok tốt!!!
27 tháng 2 2015
a,Gọi tổng trên là A.
Xét \(\frac{4}{5}-\frac{4}{7}=\frac{8}{35};...;\frac{4}{59}-\frac{4}{61}=\frac{8}{3599}\)=>\(A=\frac{1}{2}.\left(\frac{4}{5}-\frac{4}{7}+\frac{4}{7}-\frac{4}{9}+...+\frac{4}{59}-\frac{4}{61}\right)\)\(=\frac{1}{2}.\left(\frac{4}{5}-\frac{4}{61}\right)=\frac{1}{2}.\frac{224}{305}=\frac{112}{305}\)
b,Gọi tổng trên là B
Theo đề bài ta có:\(B=\frac{24.47-23}{24+47.23}.\frac{3+\frac{3}{7}-\frac{3}{11}+\frac{3}{1001}-\frac{3}{13}}{\frac{9}{1001}-\frac{9}{13}+\frac{9}{7}-\frac{9}{11}+9}\)=\(\frac{\left(23+1\right).47-23}{24+47.23}.\frac{3+\frac{3}{7}-\frac{3}{11}+\frac{3}{1001}-\frac{3}{13}}{\frac{9}{1001}-\frac{9}{13}+\frac{9}{7}-\frac{9}{11}+9}=\frac{47.23+24}{24+47.23}.\frac{3.\left(1+\frac{1}{7}-\frac{1}{11}+\frac{1}{1001}-\frac{1}{13}\right)}{3.\left(3+\frac{3}{1001}-\frac{3}{13}+\frac{3}{7}-\frac{3}{11}\right)}\)\(=\frac{1+\frac{1}{1001}-\frac{1}{13}+\frac{1}{7}-\frac{1}{11}}{3+\frac{3}{1001}-\frac{3}{13}+\frac{3}{7}-\frac{3}{11}}=\frac{1+\frac{1}{1001}-\frac{1}{13}+\frac{1}{7}-\frac{1}{11}}{3.\left(1+\frac{1}{1001}-\frac{1}{13}+\frac{1}{7}-\frac{1}{11}\right)}=\frac{1}{3}\)
LP
29 tháng 2 2016
\(2\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)
\(=2\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\right)\)
\(=2\left(\frac{1}{5}-\frac{1}{61}\right)=2\left(\frac{61-5}{305}\right)=2.\frac{56}{305}=\frac{112}{305}\)
10 tháng 7 2017
\(A=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{43.45}\)
\(2A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{43.45}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{43}-\frac{1}{45}\)
\(=\frac{1}{3}-\frac{1}{45}=\frac{15}{45}-\frac{1}{45}=\frac{14}{45}\)
\(\Rightarrow A=\frac{14}{45}:2=\frac{14}{90}=\frac{7}{45}\)
Vậy \(A=\frac{7}{45}\).
DP
10 tháng 7 2017
Áp dụng công thức : \(\frac{1}{a}-\frac{1}{a+n}=\frac{n}{a\left(a+n\right)}\)
\(A=\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{43\cdot45}\)
\(A=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{43}-\frac{1}{45}\right)\)
\(A=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{45}\right)\)
\(A=\frac{1}{2}\cdot\frac{14}{45}=\frac{7}{45}\)
S
3 tháng 5 2017
\(M=\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.\frac{4^2}{4.5}=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}=\frac{1}{5}\)
\(N=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{99.101}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\)
\(=\frac{1}{3}-\frac{1}{101}=\frac{98}{303}\)
3 tháng 5 2017
N=1/2x(1/3-1/5+1/5-1/7+....+1/99-1/101)
N=1/2x(1/3-1/101)
N=1/2x98/101
N=49/101
10 tháng 5 2018
A =(1/2 +1)×(1/3 +1)×(1/4 +1)×....×(1/99 +1)
=3/2x4/3x...............x100/99
=2-1/99
=197/99
10 tháng 5 2018
A= \(\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot.....\cdot\frac{100}{99}\)
A=\(\frac{\left(3\cdot4\cdot5\cdot....\cdot99\right)\cdot100}{2\cdot\left(3\cdot4\cdot5\cdot...\cdot99\right)}\)
A=\(\frac{100}{2}=50\)
\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{97\cdot99}\)
\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\)
=> \(\frac{1}{3}-\frac{1}{99}=\frac{32}{99}\)>\(\frac{32}{100}\)=32%
RC
6
6 tháng 5 2017
Ta có:\(\frac{4}{5.7}+\frac{4}{7.9}+.....+\frac{4}{59.61}\)
\(\Rightarrow2.\left(\frac{2}{5.7}+\frac{2}{7.9}+......+\frac{2}{59.61}\right)\)
\(\Rightarrow2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+....+\frac{1}{59}-\frac{1}{61}\right)\)
\(\Rightarrow2.\left(\frac{1}{5}-\frac{1}{61}\right)\)
\(\Rightarrow\frac{112}{305}\)
6 tháng 5 2017
\(\frac{4}{5.7}+\frac{4}{7.9}+...+\frac{4}{59.61}\)
\(=\frac{4.2}{5.7.2}+\frac{4.2}{7.9.2}+...+\frac{4.2}{59.61.2}\)
\(=\frac{4}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)
\(=\frac{4}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}_{ }\right)\)
\(=\frac{4}{2}.\left(\frac{1}{5}-\frac{1}{60}\right)\)
\(=\frac{4}{2}.\frac{11}{60}\)
\(=\frac{11}{30}\)
TT
0
ai nhanh mik chọn nha