Cho V = 1/1*2+1/3*4+1/5+6+...+1/2015*2016 và Y = 1/1008+1/1009+1/1010+...+1/2016.Tính V:Y
Những câu hỏi liên quan
Cho S=1-1/2+1/3-1/4+...+1/2013-1/2014+1/2015
Và P=1/1008+1/1009+1/1010+...+1/2014+1/2015
Tính (S-P)^2016
Theo đầu bài ta có:
\(S=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2013}-\frac{1}{2014}+\frac{1}{2015}\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2013}+\frac{1}{2014}+\frac{1}{2015}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2014}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2013}+\frac{1}{2014}+\frac{1}{2015}\right)-\left(1+\frac{1}{2}+...+\frac{1}{1007}\right)\)
\(=\frac{1}{1008}+\frac{1}{1009}+...+\frac{1}{2015}\)
\(\Rightarrow S=P\)
Vậy ( S - P )2016 = 02016 = 0
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Cho S= 1+1/2+1/3-1/4+...+1/2003-1/2004
P=1/1008+1/1009+1/1010+...+1/2014+1/2015
Tính (S-P)2016
Tính : A=(1/1009+1/1010+...+1/2015+1/2016):(1/1-1/2+1/3-1/4+...+1/2015+1/2016)
cho S=1-1/2+1/3-1/4+......+1/2015-1/2016+1/2017 và P=1/1009+1/1010+.....+1/2016+1/2017
Tính (S-P)^2016
Tính A=(1/1009+1/1010+...+1/2016+1/2017)(1-1/2+1/3+1/4+...+1/2015+1/2016)
Cho A=1/1.2+1/3.4+1/5.6+...+1/2015.2016 và B=1/1008+2/1009+1/1010+...+1/2016. Tính B-A
\(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{2015.2016}\)
\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{2015}-\frac{1}{2016}\)
\(A=\left(1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+...+\frac{1}{2015}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{2016}\right)\)
\(A=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2015}+\frac{1}{2016}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{2016}\right)\)
\(A=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2015}+\frac{1}{2016}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{1008}\right)\)
\(A=\frac{1}{1009}+\frac{1}{1010}+\frac{1}{1011}+...+\frac{1}{2015}+\frac{1}{2016}\)
\(\Rightarrow B-A=\left(\frac{1}{1008}+\frac{1}{1009}+\frac{1}{1010}+...+\frac{1}{2016}\right)-\left(\frac{1}{1009}+\frac{1}{1010}+\frac{1}{1011}+...+\frac{1}{2016}\right)\)
\(\Rightarrow B-A=\frac{1}{1008}\)
A=(1/1009+1/1010+...+1/2015+1/2016):(1/1-1/2+1/3-1/4+...+1/2015-1/2016)
Xét số chia: 1-\(\frac{1}{2}\) + \(\frac{1}{3}\) - \(\frac{1}{4}\) +...+\(\frac{1}{2015}\) - \(\frac{1}{2016}\)
= (1+\(\frac{1}{2}\) + \(\frac{1}{3}\) + \(\frac{1}{4}\) +...+\(\frac{1}{2015}\) + \(\frac{1}{2016}\)) - 2.(\(\frac{1}{2}\) + \(\frac{1}{4}\) + ... + \(\frac{1}{2016}\))
= (1+\(\frac{1}{2}\) + \(\frac{1}{3}\) + \(\frac{1}{4}\) +...+\(\frac{1}{2015}\) + \(\frac{1}{2016}\)) - (1+\(\frac{1}{2}\) + \(\frac{1}{3}\) + \(\frac{1}{4}\) +...+\(\frac{1}{1007}\) + \(\frac{1}{1008}\))
=\(\frac{1}{1009}\) + \(\frac{1}{1010}\) + ... + \(\frac{1}{2015}\)+ \(\frac{1}{2016}\) => A=1
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Tính tổng 1/1008 + 1/1009 + 1/1010+...+ 1/2016
Cho S=\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+.........+\frac{1}{2013}-\frac{1}{2014}+\frac{1}{2015}\)
P=\(\frac{1}{1008}+\frac{1}{1009}+\frac{1}{1010}+...........+\frac{1}{2014}+\frac{1}{2015}\)
Tính (S-P)2016
\(S=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2013}-\frac{1}{2014}+\frac{1}{2015}\)
\(S=\left(1+\frac{1}{3}+...+\frac{1}{2013}+\frac{1}{2015}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2014}\right)\)
\(S=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}+\frac{1}{2014}+\frac{1}{2015}\right)-2.\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2014}\right)\)
\(S=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2014}+\frac{1}{2015}\right)-\left(1+\frac{1}{2}+...+\frac{1}{1007}\right)\)
\(S=\frac{1}{1008}+\frac{1}{1009}+...+\frac{1}{2015}\)
\(\Rightarrow\left(S-P\right)^{2016}=\left(\frac{1}{1008}+\frac{1}{1009}+...+\frac{1}{2015}-\frac{1}{1008}-\frac{1}{1009}-...-\frac{1}{2015}\right)^{2016}=0^{2016}=0\)
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Ta thấy:
\(S=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2013}-\frac{1}{2014}+\frac{1}{2015}\)
\(S=\left(1+\frac{1}{3}+...+\frac{1}{2013}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2014}\right)+\frac{1}{2015}\)
\(S=\left(1+\frac{1}{3}+...+\frac{1}{2013}\right)+\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2014}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2014}\right)+\frac{1}{2015}\)
\(S=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2013}+\frac{1}{2014}\right)-\left(1+\frac{1}{2}+...+\frac{1}{1007}\right)+\frac{1}{2015}\)
\(S=\frac{1}{1008}+\frac{1}{1009}+\frac{1}{1010}+...+\frac{1}{2014}+\frac{1}{2015}\)
Mà \(P=\frac{1}{1008}+\frac{1}{1009}+\frac{1}{1010}+...+\frac{1}{2014}+\frac{1}{2015}\) nên:
\(S=P\)\(\Rightarrow S-P=0\)\(\Rightarrow\left(S-P\right)^{2016}=0\)
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