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a)S=1+(-1/7)^1+(-1/7)^2+...+(-1/7)^2007
=>7S=7+(-1/7)^1+(1/7)^2+...+(-1/7)^2006
=>(7-1)S=6-(1/7)^2007
=>S=1-(-1/7^2007/6)
\(S=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2011}-\frac{1}{2012}+\frac{1}{2013}\)
\(=\left(1+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2013}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2012}\right)\)
\(=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}+\frac{1}{2013}-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2012}\right)\)
\(=1+\frac{1}{2}+...+\frac{1}{2012}+\frac{1}{2013}-\left(1+\frac{1}{2}+...+\frac{1}{1006}\right)\)
\(=\frac{1}{1007}+\frac{1}{1008}+...+\frac{1}{2012}+\frac{1}{2013}\)
=> S = P => (S - P)2013 = 0
\(S=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{2011}-\frac{1}{2012}+\frac{1}{2013}\)
\(\Rightarrow S=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2012}\right)\)
\(\Rightarrow S=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}-1-\frac{1}{2}-\frac{1}{3}-...-\frac{1}{1006}\)
\(\Rightarrow S=\frac{1}{1007}+\frac{1}{1008}+...+\frac{1}{2012}+\frac{1}{2013}\)\(=P\)
\(\Rightarrow\left(S-P\right)^{2013}=0^{2013}=0\)
Tík cho mik nha!
S=1-1/7-(1/7)^3-......-(1/7)^2017
49S=49-7-1/7-(1/7)^3-.,.....-(1/7)^2015
49S-S=48S=49-7-1-(1/7)^2017
48S=41-(1/7)^2017
S=41/48-(1/7)^2017/48
k nha
S= -(1/7^0 + 1/7^1+ 1/7^2 + 1/7^3 +...+ 1/7^2016)
Xét A = 1/7^0 + 1/7^1 + 1/7^2 + 1/7^3 +...+ 1/7^2016
=>7A= 7 + 1/7^0 + 1/7^1 + ...+ 1/7^2015
=> 6A = 7 - 1/7^2016
=> A = (7 - 1/7^2016)/6
=>S=-(7-1/7^2016)/6
\(S=\left(-\frac{1}{7}\right)^0+\left(-\frac{1}{7}\right)^1+...+\left(-\frac{1}{7}\right)^{2007}\)
\(-\frac{1}{7}S=\left(-\frac{1}{7}\right)^1+\left(-\frac{1}{7}\right)^2+...+\left(-\frac{1}{7}\right)^{2008}\)
\(-\frac{1}{7}S-S=\left(-\frac{1}{7}\right)^0+\left(-\frac{1}{7}\right)^{2008}\)
\(-\frac{8}{7}S=1+\frac{\left(-1\right)^{2008}}{7^{2008}}=1+\frac{1}{7^{2008}}=\frac{7^{2008}+1}{7^{2008}}\)
\(S=\frac{7^{2008}+1}{7^{2008}}:\left(-\frac{8}{7}\right)\)
HOK TOT