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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
Ta có :\(\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+...+\frac{5}{601.607}\right)\)\(\ne0\)
\(\Rightarrow x=0\)
\(X:\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+......+\frac{5}{601.607}\right)=0\)
\(\Rightarrow X:\left(\frac{5}{1}-\frac{5}{7}+\frac{5}{7}-\frac{5}{13}+\frac{5}{13}+......+\frac{5}{601}-\frac{5}{607}\right)=0\)
\(\Leftrightarrow X:\left(5-\frac{5}{607}\right)=0\)
\(\Leftrightarrow X:\frac{3030}{607}=0\)
\(\Leftrightarrow X=0\)
CÁCH 2:\(X:\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+....+\frac{5}{601.607}\right)=0\)
\(\Leftrightarrow X=0.\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+....+\frac{5}{601.607}\right)\)
\(\Leftrightarrow X=0\)
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
\(M=\frac{16}{1.5}+\frac{16}{5.9}+........+\frac{16}{2017.2021}\)
\(M=4.\left(\frac{4}{1.5}+\frac{4}{5.9}+.......+\frac{4}{2017.2021}\right)\)
\(M=4.\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+.........+\frac{1}{2017}-\frac{1}{2021}\right)\)
\(M=4.\left(1-\frac{1}{2021}\right)\)
\(M=4.\frac{2020}{2021}\)
\(M=\frac{8080}{2021}\)
\(N=\frac{1}{1.7}+\frac{1}{7.13}+.......+\frac{1}{2007.2013}\)
\(N=\frac{1}{6}.\left(\frac{6}{1.7}+\frac{6}{7.13}+........+\frac{6}{2007.2013}\right)\)
\(N=\frac{1}{6}.\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+......+\frac{1}{2007}-\frac{1}{2013}\right)\)
\(N=\frac{1}{6}.\left(1-\frac{1}{2013}\right)\)
\(N=\frac{1}{6}.\frac{2012}{2013}\)
\(N=\frac{1006}{6039}\)
\(N=\frac{1}{1.7}+\frac{1}{7.13}+...+\frac{1}{2007.2013}\)
\(N=\frac{1}{1}-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+...+\frac{1}{2007}-\frac{1}{2013}\)
\(N=1-\frac{1}{2013}\)
\(N=\frac{2012}{2013}\)
\(S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{2^n}=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^n}\)
=>\(\frac{S}{2}=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{n+1}}\)
=> \(\frac{S}{2}-S=\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+..+\frac{1}{2^{n+1}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+..+\frac{1}{2^n}\right)\)
=> \(-\frac{S}{2}=\frac{1}{2^{n+1}}-1\)
=> S= \(2-\frac{1}{2^n}\)
