\(C=\dfrac{1}{3}+\dfrac{1}{3^2}+....+\dfrac{1}{3^{20}}\\ \Rightarrow3.C=1+\dfrac{1}{3}+...+\dfrac{1}{3^{19}}\\ \Rightarrow3.C-C=\left(1+\dfrac{1}{3}+...+\dfrac{1}{3^{19}}\right)-\left(\dfrac{1}{3}+...+\dfrac{1}{3^{20}}\right)\\ =1-\dfrac{1}{3^{20}}< 1\\ \Rightarrow2C< 1\\ \Rightarrow C< \dfrac{1}{2}\)
1.Tính nhanh:
A= \(\dfrac{\dfrac{2}{3}-\dfrac{1}{4}+\dfrac{5}{11}}{\dfrac{5}{12}+1-\dfrac{7}{11}}\)
2. Cho: B =\(\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{19}\) .Hãy chứng tỏ rằng B > 1.
3. Rút gọn:
a) C= \(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right)....\left(1-\dfrac{1}{20}\right)\)
b) D= \(1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2012}}\)
4. So sánh: E=\(\dfrac{20^{10}+1}{20^{10}-1}\) và F =\(\dfrac{20^{10}-1}{20^{10}-3}\)
5. Tính giá trị của biểu thức:
M= \(\dfrac{\dfrac{3}{5}+\dfrac{3}{7}-\dfrac{3}{11}}{\dfrac{4}{5}+\dfrac{4}{7}-\dfrac{4}{11}}\)
CMR:(1+1/2).(1+1/22).(1+1/23)...(1+1/22020)<3
A= 3/2*5 + 3/5*8 +.....+ 3/17*20
B= 1/2 + 1/22 +1/23 +......+ 1/212
C= 1 + 1/2 + 1/22 + 1/23 +......+ 1/218
D= 7/10 + 7/102 + 7/103 + .......+7/1012
GIÚP MINH VỚI MÌNH CẦN GẤP!!
a) \(\dfrac{2}{1^2}.\dfrac{6}{2^2}.\dfrac{12}{3^2}.\dfrac{20}{4^2}.\dfrac{30}{5^2}.....\dfrac{110}{10^2}.x=-20\)
b) \(\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2013}\right).x+2013=\dfrac{2014}{1}+\dfrac{2015}{2}+...+\dfrac{4025}{2012}+\dfrac{4026}{2013}\)
c) \(\left(\dfrac{1}{1.2}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\right).x=\dfrac{2012}{51}+\dfrac{2012}{52}+...+\dfrac{2012}{99}+\dfrac{2012}{100}\)
Cho A=\(\frac{1}{2^2}\)+\(\frac{1}{3^2}\)+\(\frac{1}{4^2}\)+...+\(\frac{1}{20^2}\). Chứng tỏ rằng A<1.
A=\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{n^2}\)
CMR: \(\dfrac{2}{5}< A< \dfrac{8}{9}\)
1/10+1/40+1/88+...+1/(x+2)(x+5)=3/20
Tìm x, biết:
a).\(\left(\dfrac{1}{1.101}+\dfrac{1}{2.102}+...+\dfrac{1}{10.110}\right).x=\dfrac{1}{1.11}+\dfrac{1}{2.12}+...+\dfrac{1}{100.110}\)
b).\(x-\dfrac{20}{11.13}-\dfrac{20}{13.15}-\dfrac{20}{15.17}-...-\dfrac{20}{53.55}=\dfrac{3}{11}\)
c).\(\dfrac{x-1}{99}+\dfrac{x-2}{98}+\dfrac{x-5}{95}=3+\dfrac{1}{99}+\dfrac{1}{98}+\dfrac{1}{95}\)
Mấy bạn tính nhanh, hợp lí, giải ra từng bước dùm mik nha
Thanks m.n
Chứng tỏ rằng:
a) \(S=\dfrac{1}{5}+\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}+\dfrac{1}{61}+\dfrac{1}{62}+\dfrac{1}{63}< \dfrac{1}{2}\)
b) \(S=\dfrac{1}{41}+\dfrac{1}{42}+...+\dfrac{1}{80}>\dfrac{7}{12}\)
c) \(S=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{20}}< 1\)
d) \(\dfrac{49}{100}< S=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{99^2}< 1\)
Các bạn giải ra từng bước dùm mik nha
Thanks m.n
