\(\dfrac{66}{210}\)- \(\dfrac{245}{210}\)= ...............
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16 tháng 6 2023
=>16x+9y=840 và 210/x-210/y=7/4
=>16x=840-9y và 30/x-30/y=1/4
=>x=-9/16y+52,5 và (30y-30x)=xy/4
=>xy=120y-120x
=>y(-9/16y+52,5)=120y-120(-9/16y+52,5)
=>-9/16y^2+52,5y-120y+120(-9/16y+52,5)=0
=>-9/16y^2-67,5y-67,5y+6300=0
=>y=40 hoặc y=-280
=>x=30 hoặc x=210
21 tháng 7 2017
+) \(A=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{10}}\)
\(\Rightarrow2A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\)
\(\Rightarrow2A-A=\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{10}}\right)\)
\(\Rightarrow A=1-\dfrac{1}{2^{10}}=\dfrac{2^{10}-1}{2^{10}}\)
Vậy \(A=\dfrac{2^{10}-1}{2^{10}}\)
+) \(F=\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+...+\dfrac{1}{190}\)
\(\Rightarrow\dfrac{1}{2}F=\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+...+\dfrac{1}{380}\)
\(=\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+...+\dfrac{1}{19.20}=\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+...+\dfrac{1}{19}-\dfrac{1}{20}\)
\(=\dfrac{1}{5}-\dfrac{1}{20}=\dfrac{3}{20}\Rightarrow F=\dfrac{3}{20}:\dfrac{1}{2}=\dfrac{3}{10}\)
Vậy \(F=\dfrac{3}{10}\)
+) \(G=\dfrac{12}{84}+\dfrac{12}{210}+\dfrac{12}{390}+...+\dfrac{12}{2100}\)
\(=\dfrac{4}{28}+\dfrac{4}{70}+\dfrac{4}{130}+...+\dfrac{4}{700}=\dfrac{4}{4.7}+\dfrac{4}{7.10}+...+\dfrac{4}{25.28}\)
\(=\dfrac{4}{3}.\left(\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{25.28}\right)\)
\(=\dfrac{4}{3}.\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{25}-\dfrac{1}{28}\right)\)
\(=\dfrac{4}{3}.\left(\dfrac{1}{4}-\dfrac{1}{28}\right)=\dfrac{4}{3}.\dfrac{3}{14}=\dfrac{2}{7}\)
Vậy \(G=\dfrac{2}{7}\)
21 tháng 7 2017
\(A=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{10}}\)
\(2A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\)
\(2A-A=\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{10}}\right)\)
\(A=1-\dfrac{1}{2^{10}}=\dfrac{1024-1}{1024}=\dfrac{1023}{1024}\)
\(F=\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+...+\dfrac{1}{190}\)
\(=\dfrac{2}{30}+\dfrac{2}{42}+\dfrac{2}{56}+...+\dfrac{2}{380}\)
\(=\dfrac{2}{5.6}+\dfrac{2}{6.7}+\dfrac{2}{7.8}+...+\dfrac{2}{19.20}\)
\(=2\left(\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+...+\dfrac{1}{19.20}\right)\)
\(=2\left(\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{19}-\dfrac{1}{20}\right)\)
\(=2\left(\dfrac{1}{5}-\dfrac{1}{20}\right)=2.\dfrac{3}{20}=\dfrac{3}{10}\)
\(G=\dfrac{12}{84}+\dfrac{12}{210}+\dfrac{12}{390}+...+\dfrac{12}{2100}\)
\(=\dfrac{4}{28}+\dfrac{4}{70}+\dfrac{4}{130}+...+\dfrac{4}{700}\)
\(=\dfrac{4}{4.7}+\dfrac{4}{7.10}+\dfrac{4}{10.13}+...+\dfrac{4}{25.28}\)
\(=\dfrac{4}{3}\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+...+\dfrac{1}{25}-\dfrac{1}{28}\right)\)
\(=\dfrac{4}{3}\left(\dfrac{1}{4}-\dfrac{1}{28}\right)\)
\(=\dfrac{4}{3}.\dfrac{3}{14}=\dfrac{2}{7}\)
L
11 tháng 1 2022
= \(\dfrac{44}{105}\) < \(\dfrac{x}{210}\) <\(\dfrac{158}{105}\) = \(\dfrac{88}{210}< \dfrac{x}{210}< \dfrac{316}{210}\)
=> x = 89 -> 315
23 tháng 5 2022
\(=\left(\dfrac{1}{21}+\dfrac{1}{210}+\dfrac{1}{2010}\right)\cdot\dfrac{10-6-3-1}{30}=0\)
C
23 tháng 5 2022
\(\left(\dfrac{1}{3}-\dfrac{1}{5}-\dfrac{1}{10}-\dfrac{1}{30}\right)\times\left(\dfrac{1}{21}+\dfrac{1}{210}+\dfrac{1}{2010}\right)\)
\(=\left(\dfrac{10}{30}-\dfrac{6}{30}-\dfrac{3}{30}-\dfrac{1}{30}\right)\times\left(\dfrac{1}{21}+\dfrac{1}{210}+\dfrac{1}{2010}\right)\)
\(=0\times\left(\dfrac{1}{21}+\dfrac{1}{210}+\dfrac{1}{2010}\right)\)
\(=0\)
NT
1
HV
5 tháng 3 2018
Có:
\(\dfrac{n}{n+2}< \dfrac{n-1}{n}\)(Vì
\(n^2< n^2+n-2\forall n>2\))
Nên ta có
\(F=\dfrac{1}{3}.\dfrac{4}{6}....\dfrac{208}{201}\)
\(\Rightarrow F< \dfrac{1}{3}.\dfrac{3}{4}.\dfrac{6}{7}...\dfrac{207}{208}\)
\(\Rightarrow F^2< \dfrac{1.4.7...208}{3.6.9.12...210}.\dfrac{1.3.6.9...207}{3.4.7.10.208}\)
\(\Rightarrow F^2=\dfrac{1}{210}.\dfrac{1}{3}\)
\(\Rightarrow F^2=\dfrac{1}{630}< \left(\dfrac{1}{25}\right)^2\)
Vậy F\(< \dfrac{1}{25}\)
11 tháng 5 2022
X(X-1) =420
=> X^2 - X -420 = 0
=> (X+20)(X-21) =0
=> X+20 = 0 hoặc X-21 =0
=> X = -20 hoặc X = 21
RP
1
TT
4 tháng 1 2018
Ta có : x/10=63/210
=>x=(63:210).10=3
làm tương tự
=>y=40
=>t=24
\(=\dfrac{-179}{210}\)
\(\dfrac{66}{210}-\dfrac{245}{210}=\dfrac{66-245}{210}=\dfrac{-179}{210}\)