Rút gọn:
A =\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)
B = \(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\)
So sánh :
\(A=\frac{20^{10}+1}{20^{10}-1}vàB=\frac{20^{10}-1}{20^{10}-3}\)
so sánh: A với B, C với D, E với F
a,A=\(\frac{10^{19}+1}{10^{20}+1}\) B=\(\frac{10^{20}+1}{10^{21}+1}\)
b, C=\(\frac{9^{2015}+3}{9^{2014}+3}\) D= \(\frac{2^{2016}+3}{2^{2015}+3}\)
c E=\(\frac{20^{10}+1}{20^{10}-1}\) F=\(\frac{20^{10}-1}{20^{10}-3}\)
Bài 1 :So sánh
M=\(\frac{1}{2}\)+ \(\frac{1}{6}\)+..........+\(\frac{1}{2450}\) với 1
Bài 2:Rút gọn
1+\(\frac{1}{2}\)+\(\frac{1}{2^2}\)+ ........+ \(\frac{1}{2^{2012}}\)
Bài 3 : So sánh
A=\(\frac{20^{10}+1}{20^{10}-1}\)và B=\(\frac{20^{10}-1}{20^{10}-3}\)
Bài 4 :
Tìm n thuộc Z để \(\frac{3n+1}{3n+1}\)là số nguyên
Bài 5:
Chứng minh rằng phân số sau \(\frac{2n+1}{3n+1}\)là phân số tối giản với n thuộc Z
Bài 1. Tính giá trị của biểu thức sau:
A=\(\frac{7}{4}.\left(\frac{3333}{1212}+\frac{3333}{2020}+\frac{3333}{3030}+\frac{3333}{4242}\right)\)
Bài 2. So sánh
A=\(\frac{20^{10}+1}{20^{10}-1}\)
B=\(\frac{20^{10}-1}{20^{10}-3}\)
Bài 3.Tính nhanh
P=\(\frac{\frac{2}{3}-\frac{1}{4}+\frac{5}{11}}{\frac{5}{12}+1-\frac{7}{11}}\)
1 . Tinh : a , \(\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{14}\right).....\left(1-\frac{1}{5050}\right)\)b,\(\frac{^{2^{19}}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(3.2^2\right)^{10}}\)c,\(\frac{18.\frac{19}{2}.\frac{20}{3}.\frac{21}{4}.....\frac{36}{19}}{20.\frac{21}{2}.\frac{22}{3}.....\frac{36}{17}}\)giup mjk nha mjk tjk cho
1 CMR:
B=\(\frac{4}{3}+\frac{7}{3^2}+\frac{10}{3^3}+.....+\frac{3n+1}{3^n}< \frac{11}{4}\)(n thuộc N*;n>3)
A=\(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}< \frac{3}{4}\)
C=\(\frac{2}{3}+\frac{8}{9}+\frac{26}{27}+...+\frac{3^{20}-1}{3^{20}}>19\frac{1}{2}\)
B1:
Cho A = \(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}\). Hãy chứng tỏ rằng A > 1
B2:
So sánh: \(B=\) \(\frac{20^{10}+1}{20^{10}-1}\)và \(C=\frac{20^{10}-1}{20^{10}-3}\)
Tìm x biết:
a,\(\frac{1}{2a^2+1}:x=2\)
b,\(x-\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}.........-\frac{20}{53.55}=\frac{3}{11}\)
c,\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+........+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)
Tính
a. S= 3 + \(\frac{3}{2}+\frac{3}{2^2}+......+\frac{3}{2^9}\)
b. A= \(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}+\frac{1}{156}\)
c.M=\(\frac{20}{112}+\frac{20}{280}+\frac{20}{520}+\frac{20}{832}\)