So Sánh S=\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+.........+\frac{1}{2013.2014.2015}\)với \(\frac{1}{4}\)
A= \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+.....+\frac{1}{2014.2015.2016}.\)So sánh A với 1/4
Tìm x biết
\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2013.2014.2015}\right)x=\left(1.2+2.3+3.4+.....+2014.2015\right)\)
\(\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+....+\frac{1}{2013.2014}-\frac{1}{2014.2015}\right)x=\frac{1}{3}\left(2014.2015.2016-2013.2014.2015........+2.3.4-1.2.3+1.2.3-0.1.2\right)\)
\(\left(\frac{1}{2}-\frac{1}{2014.2015}\right)x=\frac{1}{3}.2014.2015.2016\)
\(x=\frac{1}{3.2029104}.2014^2.2015^2.2016=\)
\(\left(\frac{1}{2}-\frac{1}{2014.2015}\right)x=\frac{1}{3}.2014.2015.2016\)
so sánh :S= \(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{2010.2011.2012}\)với P=\(\frac{1}{2}\)
S=1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 +...+ 1/2010.2011 - 1/2011.2012
S=1/1.2 - 1/2011.2012<1/2
=>S<P
\(S=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+........+\frac{2}{2010.2011.2012}\)
\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+......+\frac{1}{2010.2011}-\frac{1}{2011.2012}\)
\(=\frac{1}{1.2}-\frac{1}{2011.2012}\)
\(=\frac{1}{2}-\frac{1}{2011.2012}\)
mà \(\frac{1}{2}-\frac{1}{2011.2012}< \frac{1}{2}\)
\(\Rightarrow S< P\)
so sánh \(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2012.2013.2014}\) với \(\frac{1}{4}\)
Lời giải:
$2A=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{2014-2012}{2012.2013.2014}$
$=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2012.2013}-\frac{1}{2013.2014}$
$=\frac{1}{1.2}-\frac{1}{2013.2014}=\frac{1}{2}-\frac{1}{2013.2014}<\frac{1}{2}$
$\Rightarrow A< \frac{1}{4}$
Cho A=\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+......+\frac{1}{2014.2015.2016}\)
So sánh với \(\frac{1}{4}\)
giúp mk nhé !
Ta có :
\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2014.2015.2016}\)
\(\Rightarrow2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{2014.2015.2016}\)
\(\Rightarrow2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2014.2015}-\frac{1}{2015.2016}\)
\(\Rightarrow2A=\frac{1}{1.2}-\frac{1}{2015.2016}\)
\(\Rightarrow A=\left(\frac{1}{2}-\frac{1}{2015.2016}\right):2\)
\(\Rightarrow A=\frac{1}{4}-\frac{1}{2015.2016}\)
\(\Rightarrow A< \frac{1}{4}\)
Vậy A < \(\frac{1}{4}\)
_Chúc bạn học tốt_
Ta có:
\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+....+\frac{1}{2014+2015+2016}\)
\(2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+.....+\frac{2}{2014.2015.2016}\)
\(2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2014.2015}-\frac{1}{2015.2016}\)
\(2A=\frac{1}{1.2}-\frac{1}{2015.2016}\)
\(\Rightarrow2A< \frac{1}{1.2}=\frac{1}{2}\)
\(\Rightarrow A< \frac{1}{4}\)
Vậy ....
A=1/1.2.3+1/2.3.4+1/3.4.5+...+1/2014.2015.2016
A=1/2.(1/2.3+1/3.4+1/4.5+...+1/2014.2015+1/2015.2016)
A=1/2.(1/2.3-1/2015.2016)
A=1/2.(1/2-1/2015.2016)
A=1/4-A1/2.2015.2016<1/4
suy ra A<1/4
cho A=\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2014.2015.2016}\)so sánh A và \(\frac{1}{4}\)
giong nhu dap an minh viet khi nay do
nho k cho minh voi nha
A=1/2(2/1.2.3+2/2.3.4+...+2/2014.2015.2016)~A=1/2(1/1.2-1/2.3+1/2.3-1/3.4+...+1/2014.2015-1/2015.2016)~~A=1/2(1/1.2-1/2015.2016)~A=1/2(1/2-1/4062240)~A=1/2.2031119/4062240~A=203119/8124480. Dấu/= dấu gạch ps còn ~ là dấu xuống dòng. Còn bài này thì ko biết dung hay sai nua
so sánh \(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2012.2013.2014}\) với \(\frac{1}{4}\)
Cho \(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+.....+\frac{1}{2014.2015.2016}\)
So sánh A với \(\frac{1}{4}\)
A=1/4-1/2015.1008
=)A<4 (ĐPCM)
Nhớ k nha
A= 1 - 1/2 - 1/3 + 1/2 - 1/3 - 1/4 + 1/3 - 1/4 - 1/5 + ....... + 1/2014 - 1/2015 - 1/2016
Rồi đoạn sau tự tính tiếp nhé :)) Đến đôạn này chắc trừ được
conan mà không biết làm mấy bài này conan lởm
So sánh:
S=\(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{2009.2010.2011}\)và P=\(\frac{1}{2}\)
s=1/1*2-1/2*3+1/2*3-1/3*4+....+1/2009*2010-1/210*2011
=1/1*2-1/2010*2011
<1/1*2
\(S=\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+...+\frac{2}{2009\cdot2010\cdot2011}\)
\(S=\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{2009\cdot2010}-\frac{1}{2010\cdot2011}\)
\(S=\frac{1}{1\cdot2}-\frac{1}{2010\cdot2011}\)
\(S=\frac{1}{2}-\frac{1}{2010\cdot2011}< \frac{1}{2}\)
=> S < P