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chứng minh rằng
\(A=\frac{1}{101}+\frac{1}{102}+....+\frac{1}{199}+\frac{1}{200}< 1\)1
Cho A=\(\frac{1}{100^2}+\frac{1}{101^2}+...+\frac{1}{199^2}\)
Chứng minh:
\(\frac{1}{100}< B< \frac{1}{99}\)
Chứng minh
A= \(\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+.....+\frac{1}{199}+\frac{1}{100}< 1\) \(1\)
Chứng minh rằng:
a) \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{199}-\frac{1}{200}\)=\(\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+...+\frac{1}{200}\)
b) \(\frac{51}{2}+\frac{52}{2}+...+\frac{100}{2}=1.3.5...99\)
28 tháng 2 2016 lúc 17:05
Chứng minh rằng :
\(\frac{1}{101}+\frac{1}{102}+....+\frac{1}{199}+\frac{1}{200}<1\)
Chứng minh rằng
a)\(\frac{5}{8}<\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+...+\frac{1}{200}<\frac{3}{4}\)
b)\(\frac{1}{4}+\frac{1}{6}+\frac{1}{16}+...+\frac{1}{10000}<\frac{3}{4}\)
c)(\(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}....\frac{199}{200}\))2 <\(\frac{1}{201}\)
d)\(50<1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}...+\frac{1}{2^{100}-1}<100\)
ChoA:\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\).Chứng minh rằng A < 3/4
Chứng minh rằng:
\(\frac{1}{5}+\frac{1}{13}+\frac{1}{25}+\frac{1}{41}+...+\frac{1}{100^2+101^2}<\frac{1}{2}\)
Cho S=\(\frac{1}{5^2}-\frac{2}{5^3}+\frac{3}{5^4}-\frac{4}{5^5}+...+\frac{99}{5^{100}}-\frac{100}{5^{101}}\)
Chứng minh rằng \(S< \frac{1}{36}\)