So sánh A=4/1.2.3 + 6/2.3.4 + 8/3.4.5 + ... + 200/99.100.11 với 3/2
Những câu hỏi liên quan
11 tháng 4 2021 lúc 20:05
Cho :
\(A=\dfrac{5}{1.2.3}+\dfrac{8}{2.3.4}+\dfrac{11}{3.4.5}+...+\dfrac{6056}{2018.2019.2020}\)
Hãy so sánh A với 2
Cho S=\(\dfrac{5}{1.2.3}+\dfrac{8}{2.3.4}+\dfrac{11}{3.4.5}+...+\dfrac{6068}{2022.2023.2024}\)
So sánh S với 2
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
Đúng 0
Bình luận (0)
So sánh A với 1/4 biết:
Với A = 1/1.2.3 + 1/2.3.4 + 1/3.4.5+....+1/2014.2015.2016
A = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + ... + 1/2014.2015.2016
=> A = 1/2.(2/1.2.3 + 2/2.3.4 + 2/3.4.5 + ... + 2/2014.2015.2016)
=> A = 1/2.(1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + 1/3.4 - 1/4.5 + ... + 1/2014.2015 - 1/2015.2016)
=> A = 1/2.(1/2 - 1/2015.2016)
=> A < 1/2.1/2 = 1/4
Đúng 0
Bình luận (0)
Ta có: \(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{2014.2015.2016}\)
\(\Rightarrow2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+....+\frac{2}{2014.2015.2016}\)
\(\Rightarrow2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+....+\frac{1}{2014.2015}-\frac{1}{2015.2016}\)
\(\Rightarrow2A=\frac{1}{1.2}-\frac{1}{2015.2016}\)
\(\Rightarrow A=\left(\frac{1}{2}-\frac{1}{2015.2016}\right):2\)
\(\Rightarrow A=\frac{1}{4}-\frac{1}{2015.2016.2}\)
\(\Rightarrow A< \frac{1}{4}\)
Đúng 0
Bình luận (0)
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 = \(\frac{1}{1.2}-\frac{1}{2015.2016}\)
=> 2A < \(\frac{1}{1.2}=\frac{1}{2}\)
=> A < \(\frac{1}{4}\)
Vậy A < \(\frac{1}{4}\)
Đúng 0
Bình luận (0)
cho A= 1/1.2.3+1/2.3.4+1/3.4.5+....+1/2014.2015.2016 so sánh với 1/4
A=4949/19800 và 1/4
4949/19800 < 1/4
Xong! t*** mik đê!!!
Đúng 0
Bình luận (0)
Cho A= 1/1.2.3+1/2.3.4+1/3.4.5+...+1/2014.2015.2016. So sánh với 1/4
\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2014.2015.2016}\)
\(A=\frac{1}{2}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2015.2016}\right)\)
\(A=0,2499998...<0,25\)
\(\Rightarrow A<\frac{1}{4}\)
Đúng 0
Bình luận (0)
Cho A=1/1.2.3+1/2.3.4+1/3.4.5+...+1/2014.2015.2016 so sánh A với 1/4
Cho : A= 3/1.2.3+3/2.3.4+3/3.4.5+.....+3/2015.2016.2017 so sánh A với1
Giúp mk với nhé!
\(A=\frac{3}{1.2.3}+\frac{3}{2.3.4}+\frac{3}{3.4.5}+...+\frac{3}{2015.2016.2017}\)
\(A=\frac{3}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\frac{3}{2}.\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+\frac{3}{2}.\left(\frac{1}{3.4}-\frac{1}{4.5}\right)+...+\frac{3}{2}.\left(\frac{1}{2015.2016}-\frac{1}{2016.2017}\right)\)
\(A=\frac{3}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2015.2016}-\frac{1}{2016.2017}\right)\)
\(A=\frac{3}{2}.\left(\frac{1}{1.2}-\frac{1}{2016.2017}\right)\)
\(A=\frac{3}{4}-\frac{3}{2.2016.2017}< 1\)
Đúng 0
Bình luận (0)
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