1.Tính:a)\(\frac{2}{1.7}+\frac{2}{7.13}+\frac{2}{13.19}+....+\frac{2}{601.607}\)
b)\(S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
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Tính
a) A = \(\frac{2}{1.7}\)+\(\frac{2}{7.13}+\frac{2}{13.19}+...+\frac{2}{601.607}\)
giúp mik vs
rất đơn giản
nhân 3 vào tư và mẫu sau đó tách \(\frac{1}{3}\) ra
ta có \(\frac{1}{3}.\left(\frac{6}{1.7}+\frac{6}{7.13}+...+\frac{6}{601.607}\right)\)
=\(\frac{1}{3}.\left(\frac{1}{1}-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+...+\frac{1}{601}-\frac{1}{607}\right)\)
=1/3 . ( 1-1/207)
bây giờ tự tính nha
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\(2\left(\frac{1}{1.7}+\frac{1}{7.13}+...+\frac{1}{601.607}\right)\)
\(2.\frac{1}{6}\left(\frac{1}{1}-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+...+\frac{1}{601}-\frac{1}{607}\right)\)
\(\frac{1}{3}\left(\frac{1}{1}-\frac{1}{607}\right)\)
\(\frac{1}{3}.\frac{606}{607}=\frac{202}{607}\)
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tìm x
\(X:\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+...+\frac{5}{601.607}\right)=0\)
Ta có :\(\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+...+\frac{5}{601.607}\right)\)\(\ne0\)
\(\Rightarrow x=0\)
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\(X:\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+......+\frac{5}{601.607}\right)=0\)
\(\Rightarrow X:\left(\frac{5}{1}-\frac{5}{7}+\frac{5}{7}-\frac{5}{13}+\frac{5}{13}+......+\frac{5}{601}-\frac{5}{607}\right)=0\)
\(\Leftrightarrow X:\left(5-\frac{5}{607}\right)=0\)
\(\Leftrightarrow X:\frac{3030}{607}=0\)
\(\Leftrightarrow X=0\)
CÁCH 2:\(X:\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+....+\frac{5}{601.607}\right)=0\)
\(\Leftrightarrow X=0.\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+....+\frac{5}{601.607}\right)\)
\(\Leftrightarrow X=0\)
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tính G= \(\frac{6^2}{1.7}+\frac{6^2}{7.13}+\frac{6^2}{13.19}+...+\frac{6^2}{n\left(n+6\right)}\)
G=6(6/1.7+6/7.13+6/13.19+..+6/n(n+6) )
=6(1-1/7+1/7-1/13+1/13-1/19+....+1/n-1/n+6)
=6(1-n/n+6)
=6.6/n+6
=36/n+6
vậy G=36/n+6
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SGK Kết nối tri thức và cuộc sống
15 tháng 8 2023 lúc 19:01
Tính:
a) \({\left( {\frac{1}{5}} \right)^{ - 2}};\)
b) \({4^{\frac{3}{2}}};\)
c) \({\left( {\frac{1}{8}} \right)^{ - \frac{2}{3}}};\)
d) \({\left( {\frac{1}{{16}}} \right)^{ - 0,75}}.\)
a: \(\left(\dfrac{1}{5}\right)^{-2}=25\)
b: \(4^{\dfrac{3}{2}}=8\)
c: \(\left(\dfrac{1}{8}\right)^{-\dfrac{2}{3}}=\left(\dfrac{1}{2}\right)^{3\cdot\dfrac{-2}{3}}=\left(\dfrac{1}{2}\right)^{-2}=4\)
d: \(\left(\dfrac{1}{16}\right)^{-0.75}=\left(\dfrac{1}{2}\right)^{4\cdot\left(-0.75\right)}=\left(\dfrac{1}{2}\right)^{-3}=8\)
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M=\(\frac{16}{1.5}+\frac{16}{5.9}+....+\frac{16}{2017.2021}\) ; N =\(\frac{1}{1.7}+\frac{1}{7.13}+....+\frac{1}{2007.2013}\)
\(M=\frac{16}{1.5}+\frac{16}{5.9}+........+\frac{16}{2017.2021}\)
\(M=4.\left(\frac{4}{1.5}+\frac{4}{5.9}+.......+\frac{4}{2017.2021}\right)\)
\(M=4.\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+.........+\frac{1}{2017}-\frac{1}{2021}\right)\)
\(M=4.\left(1-\frac{1}{2021}\right)\)
\(M=4.\frac{2020}{2021}\)
\(M=\frac{8080}{2021}\)
\(N=\frac{1}{1.7}+\frac{1}{7.13}+.......+\frac{1}{2007.2013}\)
\(N=\frac{1}{6}.\left(\frac{6}{1.7}+\frac{6}{7.13}+........+\frac{6}{2007.2013}\right)\)
\(N=\frac{1}{6}.\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+......+\frac{1}{2007}-\frac{1}{2013}\right)\)
\(N=\frac{1}{6}.\left(1-\frac{1}{2013}\right)\)
\(N=\frac{1}{6}.\frac{2012}{2013}\)
\(N=\frac{1006}{6039}\)
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\(N=\frac{1}{1.7}+\frac{1}{7.13}+...+\frac{1}{2007.2013}\)
\(N=\frac{1}{1}-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+...+\frac{1}{2007}-\frac{1}{2013}\)
\(N=1-\frac{1}{2013}\)
\(N=\frac{2012}{2013}\)
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Tính nhah ---- giúp mik giải nâ các bn thank nhiều nhiềua)frac{1+frac{1}{2}+frac{1}{3}+frac{1}{4}}{1-frac{1}{2}+frac{1}{3}-frac{1}{4}}:frac{3+frac{3}{2}+frac{3}{3}+frac{3}{4}}{2-frac{2}{2}+frac{2}{3}-frac{2}{4}}+frac{1}{3}b) frac{frac{1}{3}-frac{1}{5}-frac{1}{7}}{frac{2}{3}-0,4-frac{2}{7}}+frac{frac{3}{8}-frac{3}{16}-frac{3}{32}+frac{3}{64}}{frac{1}{4}-frac{1}{8}-frac{1}{16}+frac{1}{32}}c) frac{0,4-frac{2}{9}+frac{2}{11}}{1,4-frac{7}{9}+frac{7}{11}}-frac{frac{1}{3}-0,25+frac{1}{5}}{1frac{1}{6}-0...
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Tính nhah ---- giúp mik giải nâ các bn thank nhiều nhiều
a)\(\frac{1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}}{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}}:\frac{3+\frac{3}{2}+\frac{3}{3}+\frac{3}{4}}{2-\frac{2}{2}+\frac{2}{3}-\frac{2}{4}}+\frac{1}{3}\)
b) \(\frac{\frac{1}{3}-\frac{1}{5}-\frac{1}{7}}{\frac{2}{3}-0,4-\frac{2}{7}}+\frac{\frac{3}{8}-\frac{3}{16}-\frac{3}{32}+\frac{3}{64}}{\frac{1}{4}-\frac{1}{8}-\frac{1}{16}+\frac{1}{32}}\)
c) \(\frac{0,4-\frac{2}{9}+\frac{2}{11}}{1,4-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{1}{3}-0,25+\frac{1}{5}}{1\frac{1}{6}-0,875+0,7}\)
Tính:\(\frac{1}{x}+\frac{1}{x+1}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}+\frac{32}{1+x^{32}}\)
Tính:\(S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+...\)
\(S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{2^n}=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^n}\)
=>\(\frac{S}{2}=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{n+1}}\)
=> \(\frac{S}{2}-S=\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+..+\frac{1}{2^{n+1}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+..+\frac{1}{2^n}\right)\)
=> \(-\frac{S}{2}=\frac{1}{2^{n+1}}-1\)
=> S= \(2-\frac{1}{2^n}\)
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Thực hiện phép tính :
\(\frac{2}{1-x^2}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}+\frac{32}{1+x^{32}}\)
khó quá làm sao mà trả lời đc
tự đầu mình vắt óc mà suy nghĩ
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