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\(S=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{40.43}+\frac{3}{43.46}\)
\(S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{40}-\frac{1}{43}+\frac{1}{43}-\frac{1}{46}\)
\(S=1-\frac{1}{46}< 1\)
Chứng tỏ S < 1
Ủng hộ mk nha ^_^
S = \(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+......+\frac{3}{43.46}\)
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+.....+\frac{1}{43}-\frac{1}{46}\)
\(=1-\frac{1}{46}=\frac{45}{46}< 1\)
S = 1 + 2 + 22 + 23 + ..... + 29
2S = 2 + 22 + 23 + .... + 29 + 210
2S - S = ( 2 + 22 + 23 + .... + 29 + 210 ) - ( 1 + 2 + 22 + 23 + ..... + 29 )
S = 210 - 1
Ta có :
5 . 28 = ( 4 + 1 ) . 28 = ( 22 + 1 ) . 28 = 22 . 28 + 1 . 28 = 210 + 28
=> 210 - 1 < 210 + 28
=> S < 210 + 28
ta có s=1+2+2^2+2^3+2^4+...+2^9
=>2s=2+2^2+2^3+2^4+...+2^10
=>s=(2^10-1)/2=2^9-1/2
đến đoạn này chắc bn so sánh đc rồi
A, 910 -4/910- 5
= (9-4/9)10- 5
= 77/910 - 5
910 - 2/910 - 3
=( 9-2/9 )10 - 3
= 79/910 -3
vì 77/9
a) Ta có: \(1-\frac{9^{10}-4}{9^{10}-5}=\frac{-1}{9^{10}-5}\)
\(1-\frac{9^{10}-2}{9^{10}-3}=\frac{-1}{9^{10}-3}\)
Vì \(\frac{-1}{9^{10}-5}< \frac{-1}{9^{10}-3}\Rightarrow1-\frac{9^{10}-4}{9^{10}-5}< 1-\frac{9^{10}-2}{9^{10}-3}\)
\(\Rightarrow\frac{9^{10}-4}{9^{10}-5}>\frac{9^{10}-2}{9^{10}-3}\).
b) Ta có: \(1-\frac{2.7^{10}-1}{7^{10}}=\frac{7^{10}+1}{7^{10}}\)
\(1-\frac{2.7^{10}+1}{7^{10}+1}=\frac{7^{10}}{7^{10}+1}\)
Vì \(\frac{7^{10}+1}{7^{10}}>\frac{7^{10}}{7^{10}+1}\Rightarrow1-\frac{2.7^{10}-1}{7^{10}}>1-\frac{2.7^{10}+1}{7^{10}+1}\)
\(\Rightarrow\frac{2.7^{10}-1}{7^{10}}< \frac{2.7^{10}+1}{7^{10}+1}\)
A=\(\frac{10^{2015}+1}{10^{2016}+1}\)=>10A=\(\frac{10.\left(10^{2015}+1\right)}{10^{2016}+1}\)= \(\frac{10^{2016}+10}{10^{2016}+1}\)=\(\frac{\left(10^{2016}+1\right)+9}{10^{2016}+1}\)=\(\frac{10^{2016}+1}{10^{2016}+1}+\frac{9}{10^{2016}+1}\)=1+\(\frac{9}{10^{2016}+1}\)
B=\(\frac{10^{2016}+1}{10^{2017}+1}\)=>10B=\(\frac{10.\left(10^{2016}+1\right)}{10^{2017+1}}=\frac{10^{2017}+10}{10^{2017}+1}\)= \(\frac{\left(10^{2017}+1\right)+9}{10^{2017}+1}\)=\(\frac{10^{2017}+1}{10^{2017}+1}+\frac{9}{10^{2017}+1}\)= 1+\(\frac{9}{10^{2017}+1}\)
Vì \(10^{2016}+1< 10^{17}+1\)=>\(\frac{9}{10^{2016}+1}\)>\(\frac{9}{10^{2017}+1}\)nên \(1+\frac{9}{10^{2016}+1}>1+\frac{9}{10^{2017}+1}\)=>10A>10B
Vậy A>B
Câu b:
1/5 : 1/10 - 1/3.(6/5 - 9/4)
= 1/5 x 10 - 1/3.(24/20 - 45/20)
= 2 - 1/3.(-21/20)
= 2 + 7/20
= 40/20 + 7/20
= 47/20
Câu a:
1/2.(4/3 + 2/5) - 3/4(8/9 + 13/3)
= 1/2. 4/3 + 1/2.2/5 - 3/4.8/9 - 3/4.13/3
= 2/3 + 1/5 - 2/3 - 13/4
= (2/3 - 2/3) + (1/5 - 13/4)
= 0 + 1/5 - 13/4
= 4/20 - 65/20
= - 61/20
1/5 : 1/10 - 1/3.(6/5 - 9/4)
= 1/5 x 10 - 1/3.(24/20 - 45/20)
= 2 - 1/3.(-21/20)
= 2 + 7/20
= 40/20 + 7/20
= 47/20
Ta có :
\(S=\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}>\frac{1}{10}+\frac{1}{10}+...+\frac{1}{10}=9.\frac{1}{10}=\frac{9}{10}\) ( vì 9 số \(\frac{1}{10}\) )
\(\Rightarrow\)\(S>\frac{9}{10}\)
Vậy \(S>\frac{9}{10}\)
Chúc bạn học tốt ~
Ta có:S= 1/2+1/3+1/4+...+1/10>1/10+1/10+..+1/10(9 số 10)
=> S> 9/10
mk nghĩ là vậy
1 P/S 1/10 mà sao các bạn lại ghi nhiều như thế.Giải lại giúp mình với.
Ta có:
S = \(\frac{1}{2}+\frac{1}{3}+........+\frac{1}{10}\)
\(\frac{9}{10}=\frac{1}{10}+\frac{1}{10}+......+\frac{1}{10}\)( 9 phân số \(\frac{1}{10}\))
Mà \(\frac{1}{2}+\frac{1}{3}+.........+\frac{1}{10}>\frac{1}{10}+\frac{1}{10}+...........+\frac{1}{10}\)
\(\Rightarrow S>\frac{9}{10}\)
Vậy S > \(\frac{9}{10}\)
\(S=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}>\frac{1}{10}+\frac{1}{10}+...+\frac{1}{10}\)(9 phân số ) \(=\frac{1}{10}\cdot9=\frac{9}{10}\)
\(\rightarrow S>\frac{9}{10}\)
S = 4861/2520
VÌ 9/10 = 2268/2520
NEN 481/2520 > 2268/2520 SUY RA : S > 9/10