M= \(\frac{5}{20}\)+\(\frac{5}{21}\)+\(\frac{5}{22}\)+\(\frac{5}{23}\)+\(\frac{5}{24}\)
chứng minh M >1
Chứng minh rằng:
\(3<\frac{5}{20}+\frac{5}{21}+\frac{5}{22}+\frac{5}{23}+...+\frac{5}{49}<8\)
Cho S= \(\frac{5}{20}\)+ \(\frac{5}{21}\)+ \(\frac{5}{22}\)+ \(\frac{5}{23}\) + \(\frac{5}{24}\)
Chứng minh S < 1
Mình cần gấp lắm. Giải nhanh mình tick cho ( phải có cách giải )
Sửa đề : Chứng minh : S > 1
Ta thấy : \(\frac{5}{20}>\frac{5}{21}>\frac{5}{22}>\frac{5}{23}>\frac{5}{24}\)
\(\Rightarrow S=\frac{5}{20}+\frac{5}{21}+\frac{5}{22}+\frac{5}{23}+\frac{5}{24}>\frac{5}{24}\times5=\frac{25}{24}>1\)
Vậy S > 1 (ĐPCM)
Cho S=\(\frac{5}{20}+\frac{5}{21}+\frac{5}{22}+\frac{5}{23}+\frac{5}{24}\).chứng tỏ rằng S >1
Cac bn xem minh lam nhu the này có dc điểm tuyệt đối k?
Ta có : S>5/24×5
Suy ra 5/24×5=25/24
Mà 25/24>1
Suy ra:S>25/24>1
Suy ra S>1
Cac bn tra loi thật vào nha. Co dc điểm tuyệt đối k??
trả lời thế này chắc được điểm cao đó :
Ta thấy : \(\frac{5}{20}>\frac{5}{24}\); \(\frac{5}{21}>\frac{5}{24}\); \(\frac{5}{22}>\frac{5}{24}\); \(\frac{5}{23}>\frac{5}{24}\); \(\frac{5}{24}=\frac{5}{24}\)
\(\Rightarrow\)\(S=\frac{5}{20}+\frac{5}{21}+\frac{5}{22}+\frac{5}{23}+\frac{5}{24}>\frac{5}{24}+\frac{5}{24}+\frac{5}{24}+\frac{5}{24}+\frac{5}{24}=\frac{5}{24}.5=\frac{25}{24}\)
\(S>\frac{25}{24}>\frac{24}{24}=1\)
\(\Rightarrow S>1\)
Ta có :
1<5/24x5
Mà 5/20>5/24
5/21>5/24
5/22>5/24
5/23>5/24
5/24=5/24
=>5/20+5/21+5/22+5/23+5/24>5x5/24
S>1
Chứng minh:
\(\frac{7}{12}
gọi A=1/21+1/22+1/23+...+1/40
chia A thành 2 nhóm A1 và A2( A1+A2=A)
ta có A1=1/21+1/22+1/23+...+1/30>1/30+1/30+1/30+...+1/30(có 10 phân số 1/30)
A1>10/30=1/3(1)
ta có A2=1/31+1/32+1/33+...+1/40>1/40+1/40+1/40+...+1/40(có 10 phân số 1/40)
A2>10/40=1/4(2)
từ (1)và (2) suy ra
A1+A2>1/3+1/4
A>7/12(3)
ta có A1=1/21+1/22+1/23+...+1/20<1/20+1/20+1/20+...+1/20(có 10 phân số 1/20)
A1<10/20=1/2(4)
ta có A2=1/31+1/32+1/33+...+1/40<1/30+1/30+1/30+...+1/30(có 10 phân số 1/30)
A2<10/30=1/3(5)
từ (4)và (5) suy ra
A1+A2<1/2+1/3
A<5/6(6)
từ (3),(6) suy ra 7/12<1/21+1/22+1/23+...+1/40<5/6
cái A1+1/21+1/22+1/23+1/24+1/25+...+1/30<1/20+1/20+1/20+1/20+...+1/20 nhé
Cho S =\(\frac{5}{20}+\frac{5}{21}+\frac{5}{22}+...+\frac{5}{49}\). Chứng minh : 3<S<8
Chứng minh:
\(\frac{3}{5}
So so hang trong day la:
(50-21) : 1 + 1 = 30
Gia su = 1/50 het thi tong la:
30 x 1/50 = 3/5
Vi 1/50 la so nho nhat nen tong se lon hon 3/5
Gia su tat ca deu la 1/21
Tong la:
1/21 x 30 = 30/21 = 10/7
So sanh 10/7 va 3/2, ta thay 3/2 lon hon 10/7 la 1/14 don vi
Vi 1/21 la so lon nhat nen tong se be hon 3/2
ta có:A= 1/21 + 1/22 + ... + 1/50 > 1/50 +1/50 +...+1/50=1/50 x 30 = 3/5
=> A > 3/5
lại có: A = 1/21 + 1/22 + ... + 1/50 < 1/20 + 1/20 + ... +1/20= 1/20 x 30 = 3/2
=> A <3/2
cách này là cách nhanh nhất
a)\(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{20}}\)
b)\(\frac{\frac{2}{3}+\frac{5}{7}+\frac{4}{21}}{\frac{5}{6}+\frac{11}{7}-\frac{7}{21}}\)
c)\(\left(\frac{\frac{3}{5}+\frac{3}{11}-\frac{3}{17}}{1+\frac{5}{11}-\frac{5}{17}}+\frac{\frac{4}{7}-\frac{8}{23}-\frac{12}{139}}{\frac{5}{7}-\frac{10}{23}-\frac{7}{21}}\right):3\frac{1}{5}\)
GIÚP MÌNH VỚI Ạ
b) \(\frac{\frac{2}{3}+\frac{5}{7}+\frac{4}{21}}{\frac{5}{6}+\frac{11}{7}-\frac{7}{21}}\)
\(=\frac{\frac{29}{21}+\frac{4}{21}}{\frac{101}{42}-\frac{7}{21}}\)
\(=\frac{\frac{11}{7}}{\frac{29}{14}}\)
\(=\frac{22}{29}.\)
Chúc bạn học tốt!
Chứng minh:
\(\frac{7}{12}<\frac{1}{21}+\frac{1}{22}+\frac{1}{23}+...+\frac{1}{40}<\frac{5}{6}\)
Tính giá trị biểu thức
\(1.A=\frac{1}{5}+\frac{3}{17}-\frac{4}{3}+\left(\frac{4}{5}-\frac{3}{17}+\frac{1}{3}\right)-\frac{1}{7}+\left[\frac{-14}{30}\right]\)
\(2.B=\left(\frac{5}{8}-\frac{4}{12}+\frac{3}{2}\right)-\left(\frac{5}{8}+\frac{9}{13}\right)-\left[\frac{-3}{2}\right]+\frac{7}{-15}\)
\(3.C=\frac{5}{18}+\frac{8}{19}-\frac{7}{21}+\left(\frac{-10}{36}+\frac{11}{19}+\frac{1}{3}\right)-\frac{5}{8}\)
\(4.D=\frac{1}{9}-\left[\frac{-5}{23}\right]-\left(\frac{-5}{23}+\frac{1}{9}+\frac{25}{7}\right)+\frac{50}{14}-\frac{7}{30}\)
\(5.E=\frac{1}{13}+\left(\frac{-5}{18}-\frac{1}{13}+\frac{12}{17}\right)+\left(\frac{12}{17}+\frac{5}{18}+\frac{7}{5}\right)\)
\(6.F=\frac{15}{14}-\left(\frac{17}{23}-\frac{80}{87}+\frac{5}{4}\right)+\left(\frac{12}{17}-\frac{15}{14}+\frac{1}{4}\right)\)
\(7.G=\frac{1}{25}-\frac{4}{27}+\left(\frac{-23}{27}+\frac{-1}{25}-\frac{5}{43}\right)+\frac{5}{43}-\frac{4}{7}\)
\(8.H=\frac{4}{15}-\frac{23}{28}-\left(\frac{-23}{28}+\frac{-11}{15}-\frac{29}{27}\right)-\frac{2}{27}\)
\(9.K=\frac{1}{16}-\frac{5}{21}+\left(\frac{-1}{16}+\frac{-3}{5}-\frac{-5}{21}\right)+\frac{-2}{5}+\frac{3}{4}\)
\(10.L=\frac{7}{12}+\frac{15}{14}-\left(\frac{14}{22}+\frac{-1}{14}+\frac{5}{21}\right)-\frac{-5}{21}+\frac{3}{5}\)
yutyugubhujyikiu