cho A =1/2*3/4*5/6*...*99/100
B=2/3*4/5*6/7*...*100/101
C=1/2*2/3*4/5*...*98/99
a) so sanh A, B, C
b) Chung minh: A*C< A^2< 1/10
c) Chung minh: 1/15< A< 1/10
Lam giup minh di ai lam duoc minh tich dung cho
Cho M =\(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}vaN=\frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{100}{101}\)
a) Tinh tich M.N
b) chung minh M<N
c) Chung minh M < \(\frac{1}{10}\)
c) \(M=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}< \frac{1}{2}.\frac{4}{4}.\frac{6}{6}...\frac{100}{100}=\frac{1}{2}\)
a) M . N = \(\left(\frac{1}{2.}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}\right).\left(\frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{100}{101}\right)=\frac{1.2.3.4....100}{2.3.4.5...101}=\frac{1}{101}\)
Cho A= 1/2 . 3/4 . 5/6 . ......... . 99/100
B= 2/3 . 4/5 . ......... . 100/101
Chung minh A<B
Tính nhanh : a) -1-2-3-4-5-.....-199-200-201-202 b) 1+2-3-4+5+6-7-8+9+10-11-12+13+98-99-100+101+102
Giai chi tiet giup minh nha !!! Minh tich cho !!
A = - ( 1+2+3 +....+ 202) = - 203. 101 = -20503
B= ( 1+2-3-4) + ( 5+6-7-8) +..........+( 97+98 -99-100) + ( 101+102)
= -4 + (-4) .........+ (-4) + 203
= -4 .25 + 203 = 103
cho a=1/2.3/4.5/6. ... .99/100;b=2/3.4/5. ... .100/101;c=1/2.2/3.3/4. ... 98/99 a, so sánh a, b,c b,chứng minh a.c<a^2<1/100 c,chứng minh 1/15<a<1/10
Cho minh hoi vai bai:
Bài 1: chứng minh
A=1/100+1/101+...+1/200>1/2
B=1/21+1/22+1/23+... Chung minh 5/6<B<4/3
C=1/2^2+1/3^2+...+1/99^2+1/100^2 <3/4
Bai2: tìm x, y
A) x/3-1/y=1/3
B)1/x+y/2=-1/3
C)x/5-2/y=2/15
a) Cho P=5+5^2+5^3+5^4+5^5+...+5^102 .Chứng minh P:6 b) Cho A=1+4+4^2+4^3+...+4^100 Chứng minh A:5 c) Cho B = 1+2+2^2+2^3+...2^98 Chứng minh B:7 d) Cho C =1+3+3^2+3^3+...+3^104 Chứng minh C:40
a)chung minh A= 2^1+2^2+2^3+2^4+...2^2010chia het cho 3
b)chung minh B= 3^1+3^2+3^3+3^4+...3^2010chia het cho 4
c)chung minh C= 5^1+5^2+5^3+5^4+...5^2010chia het cho 6
d)chung minh D= 7^1+7^2+7^3+7^4+...7^2010chia het cho 8
a) A=21+22+23+...+22010
A=(21+22)+(23+24)+.....+(22009+22010)
A=(21x3)+(23x3)+.....+(22009x3)
A=3x(21+23+.......+22009)
Vậy A chia hết cho 3.
NHỮNG CÂU CÒN LẠI BẠN LÀM TƯƠNG TỰ !
Cho M = 1/2 . 3/4 . 5/6 .... 99/100
N = 2/3 . 4/5 . 6/7 .... 100/101
a) chứng minh M < N
b) Tìm tích M
c) Chứng minh M < 1/10
Ai nhanh thì tick
a) Mỗi biểu thức M và N đều có 50 thừa số
Ta thấy \(\frac{1}{2}< \frac{2}{3};\frac{3}{4}< \frac{4}{5};\frac{5}{6}< \frac{6}{7};...;\frac{99}{100}< \frac{100}{101}\)
\(\Rightarrow\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}< \frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{100}{101}\)
Vậy \(M< N\)
b) \(M.N=\left(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}\right).\left(\frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{100}{101}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}.\frac{6}{7}...\frac{99}{100}.\frac{100}{101}\)
\(=\frac{1}{101}\)
c) Vì \(M< N\)nên \(M.M< M.N\)hay \(M.M< \frac{1}{101}< \frac{1}{100}\). Do đó \(M.M< \frac{1}{100}=\frac{1}{10}.\frac{1}{10}\)suy ra \(M< \frac{1}{10}\)( Vì \(M>0\))
Cho A = (1:2).(3:4).(5:60) ..... (99:100)
Cho B = (2:3).(4:5).(6:7) ..... (100:101)
Chứng minh A<B
Tính tích A , B
Chứng minh A < 1:10
a, ta xét:
\(\frac{1}{2}< \frac{2}{3}\)
\(\frac{3}{4}< \frac{4}{5}\)
\(\frac{5}{6}< \frac{6}{7}\)
.....
\(\frac{99}{100}< \frac{100}{101}\)
=>\(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.....\frac{99}{100}< \frac{2}{3}.\frac{4}{5}.\frac{6}{7}.....\frac{100}{101}\)
hay:A<B(đpcm)
b,\(A.B=\frac{1}{2}.\frac{3}{4}.....\frac{99}{100}.\frac{2}{3}.\frac{4}{5}.....\frac{100}{101}\)
\(=\frac{1.2.3....100}{2.3.4....101}=\frac{1}{101}\)
c,vì A<B (theo phần a)
=>A.A<B.A
Mà B.A=\(\frac{1}{101}\)
=>A2<101
Mà A2=\(\left(\frac{1}{2}.\frac{3}{4}.....\frac{99}{100}\right)^2\)
=>\(\left(\frac{1}{2}.\frac{3}{4}.....\frac{99}{100}\right)^2\)<\(\frac{1}{101}\)<\(\frac{1}{100}=\frac{1}{10^2}\)
=>\(\left(\frac{1}{2}.\frac{3}{4}.....\frac{99}{100}\right)^2\)<\(\frac{1}{10^2}\)
=>\(\frac{1}{2}.\frac{3}{4}....\frac{99}{100}< \frac{1}{10}\)
Hay A<\(\frac{1}{10}\)