Tính A = \(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}+\frac{1}{50}}{\frac{1}{49}+\frac{2}{48}+\frac{3}{47}+...+\frac{48}{2}+\frac{49}{1}}\)
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16 tháng 3 2018
p=\(\frac{1}{49}+\frac{2}{48}+\frac{3}{47}+...+\frac{48}{2}+49\)
=\(\left(\frac{1}{49}+1\right)+\left(\frac{2}{48}+1\right)+\left(1+\frac{3}{47}\right)+...+\left(1+\frac{48}{2}\right)+\frac{50}{50}\)
=\(\frac{50}{50}+\frac{50}{49}+\frac{50}{48}+...+\frac{50}{2}\)
=\(50\left(\frac{1}{50}+\frac{1}{49}+\frac{1}{48}+...+\frac{1}{2}\right)\)
p=50*S
\(\frac{S}{\text{p}}=\frac{1}{50}\)
6 tháng 10 2018
\(\frac{49}{1}+\frac{48}{2}+\frac{47}{3}+...+\frac{2}{48}+\frac{1}{49}\)
\(=1+1+...+1+\frac{48}{2}+\frac{47}{3}+...+\frac{2}{48}+\frac{1}{49}\)(có 49 số 1)
\(=\left(1+\frac{48}{2}\right)+\left(1+\frac{47}{3}\right)+...+\left(1+\frac{2}{48}\right)+\left(1+\frac{1}{49}\right)+1\)
\(=\frac{50}{2}+\frac{50}{3}+...+\frac{50}{48}+\frac{50}{49}+\frac{50}{50}\)
\(=50\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{49}+\frac{1}{50}\right)\)
Chúc bạn học tốt.
PD
1
7 tháng 4 2018
\(50\cdot A=\frac{49}{1}+\frac{48}{2}+\frac{47}{3}+...+\frac{2}{48}+\frac{1}{49}\)
\(50\cdot A=1+\left(\frac{48}{2}+1\right)+\left(\frac{47}{3}+1\right)+...+\left(\frac{2}{48}+1\right)+\left(\frac{1}{49}+1\right)\)
\(50\cdot A=\frac{50}{50}+\frac{50}{2}+\frac{50}{3}+...+\frac{50}{48}+\frac{50}{49}\)
\(50\cdot A=50\cdot\left(\frac{1}{50}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{48}+\frac{1}{49}\right)\)
\(\Rightarrow A=\frac{1}{2}+\frac{1}{3}+...+\frac{1}{48}+\frac{1}{49}+\frac{1}{50}\)
NA
7 tháng 4 2016
Ta có:\(P=\frac{1}{49}+\frac{2}{48}+\frac{3}{47}+....+\frac{48}{2}+\frac{49}{1}+50-50\)
\(=\left(1+\frac{1}{49}\right)+\left(1+\frac{2}{48}\right)+\left(1+\frac{3}{47}\right)+...+\left(1+\frac{48}{2}\right)+\left(1+\frac{49}{2}\right)-50\)
\(=\frac{50}{49}+\frac{50}{48}+\frac{50}{47}+....+\frac{50}{2}+\frac{50}{1}-50\)
\(=50\left(\frac{1}{49}+\frac{1}{48}+\frac{1}{47}+....+\frac{1}{2}\right)+50-50\)
\(=50\left(\frac{1}{49}+\frac{1}{48}+\frac{1}{47}+....+\frac{1}{2}\right)\)
mà \(S=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{49}\)
\(=>\frac{S}{P}=\frac{1}{50}\)
Vậy \(\frac{S}{P}=\frac{1}{50}\)
S
15 tháng 3 2017
Ta có: P = \(\frac{1}{49}+\frac{2}{48}+\frac{3}{47}+...+\frac{49}{1}\)
\(=\frac{49}{1}+\frac{48}{2}+\frac{47}{3}+...+\frac{1}{49}\)
\(=\frac{50-1}{1}+\frac{50-2}{2}+\frac{50-3}{3}+...+\frac{50-49}{49}\)
\(=\frac{50}{1}-\frac{1}{1}+\frac{50}{2}-\frac{2}{2}+\frac{50}{3}-\frac{3}{3}+...+\frac{50}{49}-\frac{49}{49}\)
\(=\left(\frac{50}{1}+\frac{50}{2}+\frac{50}{3}+...+\frac{50}{49}\right)-\left(\frac{1}{1}+\frac{2}{2}+\frac{3}{3}+...+\frac{49}{49}\right)\)
\(=50+50\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}\right)-49\)
\(=50\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}\right)+1\)
\(=50\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}\right)+\frac{50}{50}\)
\(=50\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}+\frac{1}{50}\right)\)
\(\Rightarrow\frac{S}{P}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{50}}{50\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}+\frac{1}{50}\right)}=\frac{1}{50}\)
5 tháng 4 2016
\(P=\frac{99}{50}-\frac{97}{49}+...+\frac{7}{4}-\frac{5}{3}+\frac{3}{2}-1\)
\(=2.\left(\frac{99}{100}-\frac{97}{98}+...+\frac{7}{8}-\frac{5}{6}+\frac{3}{4}-\frac{1}{2}\right)\)
\(=2\left[\left(1-\frac{1}{100}\right)-\left(1-\frac{1}{98}\right)+...+\left(1-\frac{1}{8}\right)-\left(1-\frac{1}{6}\right)+\left(1-\frac{1}{4}\right)-\left(1-\frac{1}{2}\right)\right]\)
A = \(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}+\frac{1}{50}}{\frac{1}{49}+\frac{2}{48}+\frac{3}{47}+...+\frac{48}{2}+\frac{49}{1}}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}+\frac{1}{50}}{\left(\frac{1}{49}+1\right)+\left(\frac{2}{48}+1\right)+\left(\frac{3}{47}+1\right)+...+\left(\frac{48}{2}+1\right)+\frac{50}{50}}\)
A = \(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}+\frac{1}{50}}{\frac{50}{49}+\frac{50}{48}+\frac{50}{47}+...+\frac{50}{2}+\frac{50}{50}}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}+\frac{1}{50}}{\left(\frac{1}{49}+\frac{1}{48}+\frac{50}{47}+...+\frac{1}{2}+\frac{1}{50}\right).50}=\frac{1}{50}\)
\(A=\frac{T}{M}\)
\(M=\frac{1}{49}+1+\frac{2}{48}+1+\frac{3}{47}+1+.........+\frac{48}{2}+1+1\)
\(=\frac{50}{49}+\frac{50}{48}+\frac{50}{47}+.........+\frac{50}{2}+1\)
\(=50.\left(\frac{1}{49}+\frac{1}{48}+\frac{1}{47}+......+\frac{1}{2}+\frac{1}{50}\right)=50.T\)
\(A=\frac{T}{50T}=\frac{1}{50}\)