M=1/2-1/2^4+1/2^7-1/2^10+...+1/2^49-1/2^52
so sánh M với 9/4
Cho M = 1/2-1/24+1/27-1/210+....+1/243-1/246+1/249-1/252. So sánh M với 9/4 .
1:
Biết M= \(\frac{1}{2}-\frac{1}{2^4}+\frac{1}{2^7}-\frac{1}{2^{10}}+...+\frac{1}{2^{43}}-\frac{1}{2^{46}}+\frac{1}{2^{49}}-\frac{1}{2^{52}}\)
Hãy so sánh M và \(\frac{9}{4}\)
\(M=\frac{1}{2}-\frac{1}{2^4}+\frac{1}{2^7}-\frac{1}{2^{10}}+....+\frac{1}{2^{43}}-\frac{1}{2^{46}}+\frac{1}{2^{49}}-\frac{1}{2^{52}}\)
Nên \(2^3.M=4-\frac{1}{2}+\frac{1}{2^4}-\frac{1}{2^7}+.....+\frac{1}{2^{46}}-\frac{1}{2^{52}}\)
Suy ra \(2^3.M-M=4-\frac{1}{2^{52}}\)hay\(7.M=4-\frac{1}{2^{52}}\).
Khi đó \(M=\frac{4}{7}-\frac{1}{2^{52}.7}< 1\)
Vì \(\frac{9}{4}>1;M< 1\)nên \(\frac{9}{4}>M\)
Vậy \(\frac{9}{4}>M\)
cho m=1/2!+2/3!+3/4!+4/5!+5/6!+6/7!+7/8!+8/9!+9/10!. so sánh m với 1
bài 1 : so sánh: à/ 15 và √235
b/ √17+ √15 va 7
bai 2: tìm n,m
a/ 8/27=2^n/3.3^m
b/ 1/9 ^n=1/3^8
c/ 49/100=-7/10^m
d/ 1/5^3n-1=1/25
e/ 4/7^n+2=7/4
help me...mình tick cho hengggg....
M=\(\frac{1}{2}\)-\(\frac{1}{2^4}\)+\(\frac{1}{2^7}\)-\(\frac{1}{2^{10}}\)................+\(\frac{1}{2^{43}}\)-\(\frac{1}{2^{46}}\)+\(\frac{1}{2^{49}}\)
So sánh M và \(\frac{9}{4}\)
so sánh với 1
2.tính M=4/1*5+4/5*9+4/13*17+4/17*21
so sánh M với 1
3.so sánh Q với 1
Q=1/1*2+1/2*3+...+1/99*100
cho m=1/2+2/3+3/4+4/5+...+9/10 so sánh m với 1
M = \(\frac{1}{2}\)+ \(\frac{2}{3}\)+ \(\frac{3}{4}\)+\(\frac{4}{5}\)+ \(\frac{5}{6}\)+ \(\frac{6}{7}\)+ \(\frac{7}{8}\)+ \(\frac{8}{9}\)+ \(\frac{9}{10}\)= \(\frac{17819}{2520}\)
Vậy: M > 1
\(M=\frac{1}{2}-\frac{1}{2^4}+\frac{1}{2^7}-\frac{1}{2^{10}}+......+\frac{1}{2^{\text{49}}}-\frac{1}{2^{52}}\)
so sanh m voi 9/4
nhờ giải đầy đủ nha ai làm đc mình tick cho\
Cho \(M=\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\frac{5}{6}+\frac{6}{7}+\frac{7}{8}+\frac{8}{9}+\frac{9}{10}\)
So sánh M với 1
Ta có:
1 = \(\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+............+\frac{1}{10}\)(10 phân số \(\frac{1}{10}\))
Mà \(\frac{1}{2}>\frac{1}{10};\frac{2}{3}>\frac{1}{10};............;\frac{9}{10}>10\)
\(\Rightarrow M>1\)
Vậy M > 1
Ta có:
1/2=0,5
2/3>0,6
<=>1/2+2/3>1,1>1
<=>1/2+2/3+3/4+...+9/10>1
Vì 1 = \(\frac{1}{10}+\frac{1}{10}+...+\frac{1}{10}\)
\(\Rightarrow\)M > 1 vì \(\frac{1}{2}>\frac{1}{10};\frac{2}{3}>\frac{1}{10};...;\frac{9}{10}>\frac{1}{10}\)
\(\Rightarrow M>1\)