Cho biểu thức M=1/2x3/4x5/6....................x99/100
N=2/3x4/5x6/7x..................................x..100/101
a)Chứng minh rằng M<N
b)Tìm tích M.N
Cho biểu thức
M=1/2x3/4x5/6x............x99/100
N=2/3x4/5x6/7x.....................x100/101
a)chứng minh rằng M<N
b)tìm tích của MxN
a. Vì
1/2 < 2/3
3/4 < 4/5
..........
99/100<100/101 nên M<N
b.M.N=\(\frac{1.2.3.4.........100}{2.3.4.5.........101}=\frac{1}{101}\)
chứng minh rằng M= 1/2x3/4x5/6x...x99/100
chứng minh rằng M= 1/2x3/4x5/6x...x99/100
Cho A=1/2x3/4x5/6x...x99/10
B=2/3x4/5x6/7x...x100/101
1/ So sánh A và B , A2 và A.B
2/ CMR : A<1/10
Cho A = 1/2x3/4x5/6x...x99/100 và B = 2/3x3/4x5/6x...x100/101
a) Chứng tỏ A < B
b) Từ đó chứng minh A = 1/2x3/4x5/6x...x99/100 < 1/10
Các bạn cố gắng giúp mik nhé. Thankyou:>
tính nhanh
1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7
1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7 + 1/20x21
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{6}-\dfrac{1}{7}=\dfrac{1}{2}-\dfrac{1}{7}=\dfrac{5}{14}\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{20}-\dfrac{1}{21}=\dfrac{21-2}{42}=\dfrac{19}{42}\)
Lời giải:
Gọi biểu thức số 1 là A và số 2 là B
\(A=\frac{3-2}{2\times 3}+\frac{4-3}{3\times 4}+\frac{5-4}{4\times 5}+\frac{6-5}{5\times 6}+\frac{7-6}{6\times 7}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
\(=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)
B tương tự A:
\(B=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{20}-\frac{1}{21}\)
\(=\frac{1}{2}-\frac{1}{21}=\frac{19}{42}\)
(x+1/2x3)+(X+1/3x4)+(X+1/4x5)+(X+1/5x6)=25/3
\(\left(x+\dfrac{1}{2\times3}\right)+\left(x+\dfrac{1}{3\times4}\right)+\left(x+\dfrac{1}{4\times5}\right)+\left(x+\dfrac{1}{5\times6}\right)=\dfrac{25}{3}\)
\(x+\dfrac{1}{2\times3}+x+\dfrac{1}{3\times4}+x+\dfrac{1}{4\times5}+x+\dfrac{1}{5\times6}=\dfrac{25}{3}\)
\(x\times4+\left(\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}\right)=\dfrac{25}{3}\)
\(x\times4+\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\right)=\dfrac{25}{3}\)
\(x\times4+\left(\dfrac{1}{2}-\dfrac{1}{6}\right)=\dfrac{25}{3}\)
\(x\times4+\dfrac{4}{12}=\dfrac{25}{3}\)
\(x\times4=\dfrac{25}{3}-\dfrac{4}{12}\)
\(x\times4=\dfrac{25}{3}-\dfrac{1}{3}\)
\(x\times4=\dfrac{24}{3}\)
\(x\times4=8\)
\(x=8\div4\)
\(x=2\)
:))
5-4/2x3 + 6-5/3x4 8-7/4x5+ 9-8/5x6
1/1x2 + 1/2x3 +1/3x4 +1/4x5 +1/5x6
1/1x2 + 1/2x3 + 1/3x4 +1/4x5 +1/5x6
= 1 -1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6
= 1 - 1/6 = 5/6