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Bài 1:CMR A<1
A=\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2010^2}+\frac{1}{2011^2}+\frac{1}{2012^2}<1\)
1.Tính tổngSleft(frac{-1}{7}right)^0+left(frac{-1}{7}right)^1+left(frac{-1}{7}right)^2+...+left(frac{-1}{7}right)^{2007}2.Tìm x5^x+5^{x+2}6503.CMRfrac{1}{6} frac{1}{5^2}+frac{1}{6^2}+frac{1}{7^2}+...+frac{1}{100^2} frac{1}{4}4. Cho Afrac{1}{2010}+frac{2}{2009}+frac{3}{2008}+...+frac{2009}{2}+frac{2010}{1} Bfrac{1}{2}+frac{1}{3}+frac{1}{4}+...+frac{1}{2010}+frac{1}{2011}So sánh A và B
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1.Tính tổng
\(S=\left(\frac{-1}{7}\right)^0+\left(\frac{-1}{7}\right)^1+\left(\frac{-1}{7}\right)^2+...+\left(\frac{-1}{7}\right)^{2007}\)
2.Tìm x
\(5^x+5^{x+2}=650\)
3.CMR
\(\frac{1}{6}< \frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}< \frac{1}{4}\)
4. Cho \(A=\frac{1}{2010}+\frac{2}{2009}+\frac{3}{2008}+...+\frac{2009}{2}+\frac{2010}{1}\)
\(B=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2010}+\frac{1}{2011}\)
So sánh A và B
cho A=\(\frac{1}{2010}+\frac{2}{2009}+\frac{3}{2008}+...+\frac{2009}{2}+\frac{2010}{1}\)
B=\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2010}+\frac{1}{2011}\)
tính\(\frac{a}{b}\)
b.giả sử 2^2010 có m chữ số và 5^2010 có n chữ số.tính m+n
\(A=1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+\left(\frac{3}{4}\right)^4-...-\left(\frac{3}{4}\right)^{2009}+\left(\frac{3}{4}\right)^{2010}\)
CMR: A k thuộc Z
a) CMR: \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}< \frac{3}{4}\)
b) CMR: \(\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+...+\frac{1}{\left(2n+1\right)^2}< \frac{1}{4}\)
Tính:Aleft(1-frac{1}{2010}right)left(1-frac{2}{2010}right)left(1-frac{3}{2010}right)...left(1-frac{4020}{2010}right)B3+7+13+21+31+43+57+...+9901Cleft(1-frac{4}{1^2}right)left(1-frac{4}{3^2}right)left(1-frac{4}{5^2}right)...left(1-frac{4}{2015^2}right)D1-frac{1}{1+2}-frac{1}{1+2+3}-frac{1}{1+2+3+4}-...-frac{1}{1+2+3+4+...+100}E1+2+3+4+5+6+...+1000000Giải giúp tớ với nhé! Ai giải đúng mình sẽ tick cho 3 cái.
Đọc tiếp
Tính:
\(A=\left(1-\frac{1}{2010}\right)\left(1-\frac{2}{2010}\right)\left(1-\frac{3}{2010}\right)...\left(1-\frac{4020}{2010}\right)\)
\(B=3+7+13+21+31+43+57+...+9901\)
\(C=\left(1-\frac{4}{1^2}\right)\left(1-\frac{4}{3^2}\right)\left(1-\frac{4}{5^2}\right)...\left(1-\frac{4}{2015^2}\right)\)
\(D=1-\frac{1}{1+2}-\frac{1}{1+2+3}-\frac{1}{1+2+3+4}-...-\frac{1}{1+2+3+4+...+100}\)
\(E=1+2+3+4+5+6+...+1000000\)
Giải giúp tớ với nhé! Ai giải đúng mình sẽ tick cho 3 cái.
Tinh\(\frac{\frac{2010}{1}+\frac{2009}{2}+\frac{2008}{3}+...+\frac{2}{2009}+\frac{1}{2010}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2010}+\frac{1}{2011}}\)
Cho A =\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+....+\frac{1}{99^2}\)
CMR A<1
Bài 1 : Cho A = \(\frac{1}{^{1^2}}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}\) . CMR : A < 2
Bài 2 : Cho B = \(2^1+2^2+2^3+2^4+...+2^{30}\). CMR : B chia hết cho 21