Tính tổng :
\(S=\frac{1}{2013-1}+\frac{2}{2013+1}+\frac{2^2}{2013^2+1}+\frac{2^3}{2013^{2^2}+1}+.....+\frac{2^{n+1}}{2013^{2^n}+1}\)
Những câu hỏi liên quan
Tính \(A=2013+\frac{2013}{1+2}+\frac{2013}{1+2+3}+\frac{2013}{1+2+3+4}+...+\frac{2013}{1+2+3+...+2012}\)
Ta có : 1 + 2 + 3 + ... + n = \(\frac{\left(n+1\right)n}{2}\)
Vậy nên : \(A=2013+\frac{2013}{\frac{3.2}{2}}+\frac{2013}{\frac{4.3}{2}}+...+\frac{2013}{\frac{2013.2012}{2}}\)
\(A=2013+\frac{4026}{2.3}+\frac{4016}{3.4}+...+\frac{4026}{2012.2013}\)
\(A=4026\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2012.2013}\right)\)
\(A=4026\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2012}-\frac{1}{2013}\right)\)
\(A=4026\left(1-\frac{1}{2013}\right)=4026.\frac{2012}{2013}=4024.\)
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Tính giá trị biểu thức B=\(2013+\frac{2013}{1+2}+\frac{2013}{1+2+3}+\frac{2013}{1+2+3+4}+...+\frac{2013}{1+2+3+...+2012}\)
B=2013.(1+
\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{2013}{1+2+3+...+2012}\)
B=2013(\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{2012.2013}\)
B=2013.2(\(1\frac{1}{2013}=2013.2.\frac{2012}{2013}=4024\)
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Maỳ có bị óc chó không mà bảo câu trả lời của đại ca tao là sai
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Xem thêm câu trả lời
\(\frac{\frac{2013}{2}+\frac{2013}{3}+\frac{2013}{4}+................+\frac{2013}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2011}{3}+.............+\frac{1}{2013}}\)
Tinh tổng trên
Tính nhanh B = \(2013+\frac{2013}{1+2}+\frac{2013}{1+2+3}+\frac{2013}{1+2+3+4}+...+\frac{2013}{1+2+3+4+...+2012}\)
=> B=2013. (1+\(\frac{1}{1+2}\) +\(\frac{1}{1+2+3}\) +...+ \(\frac{1}{1+2+3+...+2012}\))
=>B= 2013.(\(\frac{2}{2}\) + \(\frac{2}{2.3}\) +\(\frac{2}{3.4}\) +...+\(\frac{2}{2012.2013}\))
=>B= 2013.2.(\(\frac{1}{1.2}\) + \(\frac{1}{2.3}\) +\(\frac{1}{3.4}\) +...+\(\frac{1}{2012.2013}\))
=>B=4026. (1-\(\frac{1}{2}\) +\(\frac{1}{2}\) -\(\frac{1}{3}\) + ...+\(\frac{1}{2012}\) - \(\frac{1}{2013}\))
=>B=4026.(1-\(\frac{1}{2013}\))
=>B=4026.\(\frac{2012}{2013}\) => B=2.2012=4024 Vậy B=4024
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Tính
\(\frac{\frac{2013}{2}+\frac{2013}{3}+\frac{2013}{4}+.......+\frac{2013}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2013}{3}+.......+\frac{1}{2013}}\)
tính GTBT D=\(\frac{\frac{2013}{2}+\frac{2013}{3}+\frac{2013}{4}+...+\frac{2013}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)
\(D=\frac{\frac{2013}{2}+\frac{2013}{3}+\frac{2013}{4}+...+\frac{2013}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)
\(=\frac{2013\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{\left(\frac{2012}{2}+1\right)+\left(\frac{2011}{3}+1\right)+...+\left(\frac{1}{2013}+1\right)+1}\)
\(=\frac{2013\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2014}\right)}{\frac{2014}{2}+\frac{2014}{3}+...+\frac{2014}{2013}+\frac{2014}{2014}}\)
\(=\frac{2013\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2014}\right)}{2014\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2014}\right)}\)
\(=\frac{2013}{2014}\)
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Xem thêm câu trả lời
tính \(\frac{\frac{2013}{2}+\frac{2013}{3}+\frac{2013}{4}+\frac{2013}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)
Mình nghĩ kết quả là: 2013/2014
tk mình nhé
Chúc bạn học tốt
Mình đang cần
^.^
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Xem thêm câu trả lời
frac{frac{1}{2}+frac{1}{3}+......+frac{1}{2013}}{frac{2012}{1}+frac{2012}{2}+frac{2011}{3}+...+frac{1}{2013}}frac{frac{1}{2}+frac{1}{3}+..+frac{1}{2013}}{frac{2012}{1}+2+frac{2012}{2}+1+frac{2011}{3}+1+...+frac{1}{2013}+1-2014}frac{frac{1}{2}+frac{1}{3}+...+frac{1}{2013}}{frac{2014}{1}+frac{2014}{2}+...+frac{2014}{2013}-2014}frac{frac{1}{2}+frac{1}{3}+...+frac{1}{2013}}{2014left(1+frac{1}{2}+frac{1}{3}+...+frac{1}{2013}-1right)}frac{1}{2014}
Đọc tiếp
\(\frac{\frac{1}{2}+\frac{1}{3}+......+\frac{1}{2013}}{\frac{2012}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)
=\(\frac{\frac{1}{2}+\frac{1}{3}+..+\frac{1}{2013}}{\frac{2012}{1}+2+\frac{2012}{2}+1+\frac{2011}{3}+1+...+\frac{1}{2013}+1-2014}\)
=\(\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}}{\frac{2014}{1}+\frac{2014}{2}+...+\frac{2014}{2013}-2014}\)
=\(\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}}{2014\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}-1\right)}\)
=\(\frac{1}{2014}\)
tính tổng \(S=\frac{1}{2^{-2013}+1}+\frac{1}{2^{-2012}+1}+...+\frac{1}{2^0+1}+...+\frac{1}{2^{2012}+1}+\frac{1}{2^{2013}+1}\)
\(S=\frac{2^{2013}}{2^{2013}+1}+\frac{2^{2012}}{2^{2012}+1}+....+\frac{1}{2^{2012}+1}+\frac{1}{2^{2013}+1}\)
=(\(\frac{2^{2013}}{2^{2013}+1}+\frac{1}{2^{2013}+1}\))+(\(\frac{2^{2012}}{2^{2012}+1}+\frac{1}{2^{2012}+1}\))+...+ \(\frac{1}{2}\) ( có 2013 dấu ngoặc )
= 1+ 1+.....+ \(\frac{1}{2}\) = 2013\(\frac{1}{2}\)
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