tinh nhanh 2045+4026+6039+8052
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Theo đề bài ta có:
M =(-1)+2+(-3)+4+(-5)+…+(-4025)+4026
Sắp xếp lại,ta có:
(2+4+6+...+4026)+[(-1)+(-3)+(-5)+...+(-4025)]
từ 2 đến 4026 có: (4026-2):2+1=2013
tổng 2+4+6+...+4026=(2+4026).2013:2=4054182
từ (-1) đến (-4025) có :[(-4025)-(-1)]:(-2)+1=2013
tổng (-1)+(-3)+(-5)+...+(-4025)=[(-4025)+(-1).2013:2=-4052169
=>M=4054182+(-4052169)=2013
Vậy M=2013
\(S=\frac{3}{2.3}+\frac{3}{3.6}+...+\frac{3}{2014.6039}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2013.2014}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2013}-\frac{1}{2014}\)
\(=1-\frac{1}{2014}=\frac{2013}{2014}\)
2+ (-3) + 4 + (-5) + ..... + (-4025) + 4026
= [2 + (-3)] + [4 + (-5)] + .... + [4024 + (-4025)] + 4026
= -1 x 2012 + 4026 = -2012 + 4026 = 2014
\(ĐK:x\ge2013\\ PT\Leftrightarrow\sqrt{x-2013}+2\sqrt{x-2013}=3\\ \Leftrightarrow3\sqrt{x-2013}=3\\ \Leftrightarrow\sqrt{x-2013}=1\Leftrightarrow x-2013=1\\ \Leftrightarrow x=2014\left(tm\right)\)
\(\sqrt{x-2013}+\sqrt{4x-8052}=3\)
\(\Leftrightarrow\sqrt{x-2013}+\sqrt{4\left(x-2013\right)}=3\)
\(\Leftrightarrow\sqrt{x-2013}+2\sqrt{x-2013}=3\)
\(\Leftrightarrow3\sqrt{x-2013}=3\)
\(\Leftrightarrow\sqrt{x-2013}=1\)
\(\Leftrightarrow x-2013=1\)
\(\Leftrightarrow x=2014\)
\(\frac{1}{2}=\frac{2013}{4026}\)
\(\frac{2011}{4026}< \frac{2013}{4026}\Rightarrow\frac{2011}{4026}< \frac{1}{2}\)
Huhuhu,các bạn giải nhanh giúp mik nha,mik đang cần rất gấp đó ! T^T
Dễ lắm:)
Ta có: \(\frac{1}{176}+\frac{1}{336}+\frac{1}{546}+...+\frac{1}{3416}+\frac{1}{4026}\)
\(=\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}+...+\frac{1}{56.61}+\frac{1}{61.66}\)
\(=\frac{1}{5}\cdot\left(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{56.61}+\frac{5}{61.66}\right)\)
\(=\frac{1}{5}\cdot\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{56}-\frac{1}{61}+\frac{1}{61}-\frac{1}{66}\right)\)
\(=\frac{1}{5}\cdot\left(\frac{1}{11}-\frac{1}{66}\right)\)
\(=\frac{1}{5}\cdot\frac{5}{66}=\frac{1}{66}\)
\(\frac{2014\times1008-1008}{4026+2014\times2013}=\frac{1008\times\left(2014-1\right)}{2013\times2+2014\times2013}=\frac{1008\times2013}{2013\times\left(2+2014\right)}\)
\(=\frac{1008\times2013}{2013\times2016}=\frac{1}{2}\)
Trả lời:
\(\frac{2014\times1008-1008}{4026+2014\times2013}=\frac{1008\times\left(2014-1\right)}{2013\times\left(2+2014\right)}\)
\(=\frac{1008\times2013}{2013\times2016}\)
\(=\frac{1}{2}\)