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= \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+.....+\frac{1}{2014.2015.2016}.\)So sánh A với 1/4
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
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 với \(\frac{1}{4}\).
Các bạn giúp mình với ! Thanks !
2A=\(\frac{2}{1\cdot2\cdot3}\)+\(\frac{2}{2\cdot3\cdot4}\)+\(\frac{2}{3\cdot4\cdot5}\)+...+\(\frac{2}{2014\cdot2015\cdot2016}\)
2A=\(\frac{1}{1\cdot2}\)-\(\frac{1}{2\cdot3}\)+\(\frac{1}{2\cdot3}\)-\(\frac{1}{3\cdot4}\)+\(\frac{1}{3\cdot4}\)-\(\frac{1}{4\cdot5}\)+...+\(\frac{1}{2014\cdot2015}\)-\(\frac{1}{2015\cdot2016}\)
2A=\(\frac{1}{2}\)-\(\frac{1}{2015\cdot2016}\)
A=(\(\frac{1}{2}\)-\(\frac{1}{2015\cdot2016}\)):2
A=\(\frac{1}{2}\):2-\(\frac{1}{2015\cdot2016}\):2
A=\(\frac{1}{4}\)-\(\frac{1}{2015\cdot2016\cdot2}\)<\(\frac{1}{4}\)
Vậy A<\(\frac{1}{4}\)
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:
$2A=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{2014-2012}{2012.2013.2014}$
$=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2012.2013}-\frac{1}{2013.2014}$
$=\frac{1}{1.2}-\frac{1}{2013.2014}=\frac{1}{2}-\frac{1}{2013.2014}<\frac{1}{2}$
$\Rightarrow A< \frac{1}{4}$
So Sánh S=\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+.........+\frac{1}{2013.2014.2015}\)với \(\frac{1}{4}\)
\(S=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{2013.2014.2015}\)
\(S=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{2013.2014}-\frac{1}{2014.2015}\right)\)
\(S=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2014.2015}\right)\)
\(S=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4058210}\right)\)
\(S=\frac{1}{2}.\left(\frac{2029105}{4058210}-\frac{1}{4058210}\right)\)
\(S=\frac{1}{2}.\frac{2029104}{4058210}\)
\(S=\frac{1014552}{4058210}\)
Chúc bạn học tốt !!!
Công thức :
\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{6}\right)=\frac{1}{2}.\left(\frac{3}{6}-\frac{1}{6}\right)=\frac{1}{2}.\frac{2}{6}=\frac{1}{6}=\frac{1}{1.2.3}\)
bài 1: điểm A nằm trên đường tròn (B;6cm). độ dài đoạn thẳng AB là bao nhiêu cm?
bài 2: một người mang rổ trứng đi bán. sau khi bán \(\frac{4}{9}\)số trứng và 2 quả thì còn lại 28 quả. tính số trứng mang đi bán.
bài 3: 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 \(\frac{1}{4}\).
3.
Ta có :
\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2014.2015.2016}\)
\(A=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\frac{1}{2}.\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+\frac{1}{2}.\left(\frac{1}{3.4}-\frac{1}{4.5}\right)+...+\frac{1}{2}.\left(\frac{1}{2014.2015}-\frac{1}{2015.2016}\right)\)
\(A=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2014.2105}-\frac{1}{2015.2016}\right)\)
\(A=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2015.2016}\right)\)
\(A=\frac{1}{4}-\frac{1}{2.2015.2016}< \frac{1}{4}\)
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= 1/1.2.3+ 1/2.3.4+1/3.4.5+...+1/2014.2015.2016. So Sánh A với 1/4.
A = 1 - 1/2 - 1/3 + 1/2 - 1/3 - 1/4 + ... + 1/2014 - 1/2015 - 1/2016
A = 1- 1/2016
A = 2015/2016
A > 1/4