-(2012-199+20)-(-199+20)
cho mình hỏi trong bài so sánh:199 mũ 20 và 2003 mu15 vì sao người ta lại lấy 199 mũ 20 <200 mũ 20( lấy 200 mủ 20 ở đâu)
Tìm x
\(\frac{x-199}{6}+\frac{x-199}{12}+\frac{x-199}{20}+\frac{x-199}{30}+\frac{x-199}{42}=\frac{5}{14}\)\(\frac{5}{14}\)
Mình lỡ đánh nhầm 2 lần \(\frac{5}{14}\)nha :)) chỉ 1 lần thôi
\(\frac{x-199}{6}+\frac{x-199}{12}+\frac{x-199}{20}+\frac{x-199}{30}+\frac{x-199}{42}=\frac{5}{14}\)
\(\left(x-199\right)\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)=\frac{5}{14}\)
\(\left(x-199\right)\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)=\frac{5}{14}\)
\(\left(x-199\right)\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}=\frac{5}{14}\right)\)
\(\left(x-199\right)\left(\frac{1}{2}-\frac{1}{7}\right)=\frac{5}{14}\)
\(\left(x-199\right).\frac{5}{14}=\frac{5}{14}\)
\(\Leftrightarrow x-199=1\)
\(\Leftrightarrow x=200\)
(x-20)/1*(1/2+1/3+...+1/200)/(1/199+1/998+...+199/1
20+199=?
Tính:
a) 126+(−20)+2004+(−106)126+(−20)+2004+(−106);
b) (−199)+(−200)+(−201)(−199)+(−200)+(−201).
a) 126+(−20)+2004+(−106)126+(−20)+2004+(−106)
=2004+126+[(−20)+(−106)]=2004+126+[(−20)+(−106)]
=2004+126+[−(20+106)]=2004+126+[−(20+106)]
=2004+126+(−126)=2004+126+(−126)
=2004+[126+(−126)]=2004+0=2004=2004+[126+(−126)]=2004+0=2004.
b) (−199)+(−200)+(−201)=−(199+200+201)(−199)+(−200)+(−201)=−(199+200+201)
=−(199+201+200)=−[(199+201)+200]=−(199+201+200)=−[(199+201)+200]
=−(400+200)=−600=−(400+200)=−600.
199^20 và 100^24
Lời giải:
$199^{20}< 200^{20}=100^{20}.2^{20}=100^{20}.(2^5)^4=100^{20}.32^4$
$< 100^{20}.100^4=100^{24}$
199^20 và 2013^15
Ta có:
\(199^{20}< 200^{20}\)\(;\)\(2013^{15}>2000^{15}\)
Lại có: \(200^{20}=\left(200^4\right)^5=\left(16.10^8\right)^5\)
\(2000^{15}=\left(2000^3\right)^5=\left(8.10^9\right)^5=\left(80.10^8\right)^5\)
Do \(16.10^8< 80.10^8\)
\(\Rightarrow200^{20}< 2000^{15}\)
\(\Rightarrow199^{20}< 2013^{15}\)
199^20 va 2003^15
ta có :
19920 < 20020
200015 < 200315
20020 = 2004 . 5 = ( 2004 ) 5
200015 = 20003 . 5 = ( 20003 ) 5
giờ ta so sánh 2004 và 20003
2004 = 2003 . 200
20003 = ( 200 . 10 ) 3 = 2003 . 103 = 2003 . 1000
Vì 200 < 1000
=> 2004 < 20003 mà 19920 < 20020 < 200015 < 200315 nên 19920
Ta có: 19920<20020=(8.25)20=(23.52)20=260.540
200315>200015=(16.125)15=(24.53)15=260.545
Vì 260.540<260.545 nên 20020<200015
=>19920<200315
199^20 và 2003^15