chứng minh
\(\frac{1}{5}+\frac{1}{16}+\frac{1}{25}+\frac{1}{41}+\frac{1}{60}+\frac{1}{85}+\frac{1}{113}< \frac{1}{2}\)\(\frac{1}{2}\)
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Chứng tỏ :
\(\frac{1}{5}+\frac{1}{16}+\frac{1}{25}+\frac{1}{41}+\frac{1}{60}+\frac{1}{85}+\frac{1}{113}< \frac{1}{2}\)
Chứng minh:
c.\(\frac{11}{15}< \frac{1}{21}+\frac{1}{22}+\frac{1}{23}+...+\frac{1}{59}+\frac{1}{60}< \frac{3}{2}\)
b.\(\frac{1}{5}+\frac{1}{13}+\frac{1}{25}+\frac{1}{41}+\frac{1}{61}+\frac{1}{85}+\frac{1}{113}< \frac{1}{2}\)
a.\(\frac{1}{4}+\frac{1}{16}+\frac{1}{36}+\frac{1}{64}+\frac{1}{100}+\frac{1}{144}+\frac{1}{196}< \frac{1}{2}\)
chứng minh \(\frac{1}{5}+\frac{1}{13}+\frac{1}{25}+\frac{1}{41}+\frac{1}{61}+\frac{1}{85}+\frac{1}{113}<\frac{1}{2}\)
\(\frac{1}{5}+\frac{1}{13}+\frac{1}{25}+\frac{1}{41}+\frac{1}{61}+\frac{1}{85}+\frac{1}{113}=\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{25}+\frac{1}{41}\right)+\left(\frac{1}{61}+\frac{1}{85}+\frac{1}{113}\right)\)
< \(\frac{1}{5}+\frac{1}{12}.3+\frac{1}{60}.3=\frac{1}{5}+\frac{1}{4}+\frac{1}{20}=\frac{4}{20}+\frac{5}{20}+\frac{1}{20}=\frac{10}{20}=\frac{1}{2}\)(đpcm)
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ê cho hỏi tại sao lại ra < \(\frac{1}{5}+\frac{1}{12}.3+\frac{1}{60}.3\)
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CMR:
Xem chi tiết
\(S1=\frac{1}{5}+\frac{1}{13}+\frac{1}{25}+\frac{1}{41}+\frac{1}{61}+\frac{1}{85}+\frac{1}{113}<\frac{1}{2}\)
1. so sánh
A=\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+....+với1\)
B=\(1-\left(\frac{1}{5}+\frac{1}{13}+\frac{1}{25}+\frac{1}{41}+\frac{1}{61}+\frac{1}{85}+\frac{1}{113}\right)với\frac{1}{2}\)
C=\(1-\left(\frac{1}{5}+\frac{1}{11}+\frac{1}{10}+\frac{1}{9}+\frac{1}{59}+\frac{1}{58}+\frac{1}{57}\right)với\frac{1}{2}\)
Cho P=\(\frac{1}{5}+\frac{1}{14}+\frac{1}{28}+\frac{1}{41}+\frac{1}{61}+\frac{1}{85}+\frac{1}{97}\)
Chứng minh rằng P<1/2
Chứng minh rằng:
\(\frac{1}{5}+\frac{1}{13}+\frac{1}{25}+\frac{1}{41}+...+\frac{1}{100^2+101^2}<\frac{1}{2}\)
Tính nhanh (nếu có thể):
a,frac{frac{3}{41}-frac{12}{47}+frac{27}{53}}{frac{4}{41}-frac{16}{47}+frac{36}{53}}+frac{-0,25.frac{-2}{3}-75%:(frac{-1}{2}+frac{2}{3})}{|-1frac{1}{2}|.(frac{-2}{3}-0,75:frac{3}{-2})}
b,A158.(frac{12-frac{12}{7}-frac{12}{289}-frac{12}{85}}{4-frac{4}{7}-frac{4}{289}-frac{4}{85}}:frac{5+frac{5}{13}+frac{5}{169}+frac{5}{91}}{6+frac{6}{13}+frac{6}{169}+frac{6}{91}}).frac{50550505}{711711711}
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Tính nhanh (nếu có thể):
\(a,\frac{\frac{3}{41}-\frac{12}{47}+\frac{27}{53}}{\frac{4}{41}-\frac{16}{47}+\frac{36}{53}}+\frac{-0,25.\frac{-2}{3}-75\%:(\frac{-1}{2}+\frac{2}{3})}{|-1\frac{1}{2}|.(\frac{-2}{3}-0,75:\frac{3}{-2})}\)
\(b,A=158.(\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{5+\frac{5}{13}+\frac{5}{169}+\frac{5}{91}}{6+\frac{6}{13}+\frac{6}{169}+\frac{6}{91}}).\frac{50550505}{711711711}\)
a: \(=\dfrac{3\left(\dfrac{1}{41}-\dfrac{4}{47}+\dfrac{9}{53}\right)}{4\left(\dfrac{1}{41}-\dfrac{4}{47}+\dfrac{9}{53}\right)}+\dfrac{-\dfrac{1}{4}\cdot\dfrac{-2}{3}-\dfrac{3}{4}:\dfrac{1}{6}}{\dfrac{3}{2}\cdot\left(\dfrac{-2}{3}-\dfrac{3}{4}\cdot\dfrac{-2}{3}\right)}\)
\(=\dfrac{3}{4}+\dfrac{\dfrac{2}{12}-\dfrac{9}{2}}{\dfrac{3}{2}\cdot\dfrac{-1}{6}}=\dfrac{3}{4}+\dfrac{-13}{3}:\dfrac{-3}{12}\)
\(=\dfrac{3}{4}+\dfrac{13}{3}\cdot\dfrac{12}{3}=\dfrac{3}{4}+\dfrac{156}{9}=\dfrac{217}{12}\)
b: \(A=158\left(\dfrac{12\left(1-\dfrac{1}{7}-\dfrac{1}{289}-\dfrac{1}{85}\right)}{4\left(1-\dfrac{1}{7}-\dfrac{1}{289}-\dfrac{1}{85}\right)}:\dfrac{5\left(1+\dfrac{1}{13}+\dfrac{1}{169}+\dfrac{1}{91}\right)}{6\left(1+\dfrac{1}{13}+\dfrac{1}{169}+\dfrac{1}{91}\right)}\right)\cdot\dfrac{50550505}{711711711}\)
\(=158\cdot\left(3\cdot\dfrac{6}{5}\right)\cdot\dfrac{50550505}{711711711}\)
\(\simeq40.39\)
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Tính nhanh (nếu có thể):a,frac{frac{3}{41}-frac{12}{47}+frac{27}{53}}{frac{4}{41}-frac{16}{47}+frac{36}{53}}+frac{-0,25.frac{-2}{3}-75%:(frac{-1}{2}+frac{2}{3})}{|-1frac{1}{2}|.(frac{-2}{3}-0,75:frac{3}{-2})}b,A158.(frac{12-frac{12}{7}-frac{12}{289}-frac{12}{85}}{4-frac{4}{7}-frac{4}{289}-frac{4}{85}}:frac{5+frac{5}{13}+frac{5}{169}+frac{5}{91}}{6+frac{6}{13}+frac{6}{169}+frac{6}{91}}).frac{50550505}{711711711}
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Tính nhanh (nếu có thể):
\(a,\frac{\frac{3}{41}-\frac{12}{47}+\frac{27}{53}}{\frac{4}{41}-\frac{16}{47}+\frac{36}{53}}+\frac{-0,25.\frac{-2}{3}-75\%:(\frac{-1}{2}+\frac{2}{3})}{|-1\frac{1}{2}|.(\frac{-2}{3}-0,75:\frac{3}{-2})}\)
\(b,A=158.(\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{5+\frac{5}{13}+\frac{5}{169}+\frac{5}{91}}{6+\frac{6}{13}+\frac{6}{169}+\frac{6}{91}}).\frac{50550505}{711711711}\)