Chứng minh rằng :
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{19}-\frac{1}{20}=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}\)
Tính nhanh:
A=\(\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)
B=\(\frac{3}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}\)
Chứng minh rằng:
\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}<\frac{1}{2}\)
Cho \(S=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}\)
Hãy so sánh S với \(\frac{1}{2}\)
\(\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+...+\frac{1}{19}+\frac{1}{20}+\frac{1}{21}>\frac{5}{11}\)
cho S\(=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{19}+\frac{1}{20}\)
so sánh S và \(\frac{1}{2}\)
2, Tính \(\frac{A}{B}\)
A=\(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{19.20}\)
B=\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{19}+\frac{1}{20}\)
Ai giúp với ạ
So sánh
F = \(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+......+\frac{19}{9^2.10^2}\)với 1
E = \(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}\)với \(\frac{1}{2}\)
\(S=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}\)
Hãy so sánh S và \(\frac{1}{2}\)
