cho A = \(\frac{1}{1.102}+\frac{1}{2.103}+...+\frac{1}{299.400}\)
Chứng minh A = \(\frac{1}{101}\left(1+\frac{1}{2}+...+\frac{1}{101}\right)-\left(\frac{1}{300}+\frac{1}{301}+...+\frac{1}{400}\right)\)
1/ Cho \(A=\frac{1}{1.102}+\frac{1}{2.103}+...+\frac{1}{299.400}\)
Chứng minh rằng: \(A=\frac{1}{101}\left[\left(1+\frac{1}{2}+...+\frac{1}{101}\right)-\left(\frac{1}{300}+\frac{1}{301}+...+\frac{1}{400}\frac{ }{ }\right)\right]\)
2/ Tính \(A=\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2005^2}\). Chứng minh \(A< 1\)
3/ Cho \(A=\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}\)
Chứng minh: \(\frac{1}{2}< A< 1\)
GIÚP MÌNH NHA, MÌNH ĐANG CẦN GẤP.MÌNH SẼ TICK AI NHANH NHẤT!!
1/ Cho \(A=\frac{1}{1.102}+\frac{1}{2.203}+...+\frac{1}{299.400}\)
Chứng minh rằng: \(A=\frac{1}{101}\left[\left(1+\frac{1}{2}+...+\frac{1}{101}\right)-\left(\frac{1}{300}+\frac{1}{301}+...+\frac{1}{400}\right)\right]\)
2/ Cho \(A=\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2005^2}\)
\(B=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2004.2005}\)
a) So sánh \(A\)với \(B\) b) Chứng minh: \(A< 1\)
3/ Cho \(A=\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}\)
Chứng minh: \(\frac{1}{2}< A< 1\)
GIÚP MÌNH NHA, MÌNH CẢM ƠN. MÌNH ĐANG CẦN GẤP!!!!
Tính: \(\frac{\frac{1}{1.300}+\frac{1}{2.301}+\frac{1}{3.302}+...+\frac{1}{101.400}}{\frac{1}{1.102}+\frac{1}{2.103}+\frac{1}{3.104}+...+\frac{1}{299.400}}\)
\(\frac{\frac{1}{1.300}+\frac{1}{2.301}+\frac{1}{3.302}+.............+\frac{1}{101.400}}{\frac{1}{1.102}+\frac{1}{2.103}+\frac{1}{3.104}+.......+\frac{1}{299.400}}\)
Tính: \(C=\frac{\frac{1}{1.300}+\frac{1}{2.301}+\frac{1}{3.302}+...+\frac{1}{101.4000}}{\frac{1}{1.102}+\frac{1}{2.103}+\frac{1}{3.104}+...+\frac{1}{299.400}}\)
Tính nhanh: \(\frac{\frac{1}{1.300}+\frac{1}{2.301}+...+\frac{1}{101.400}}{\frac{1}{1.102}+\frac{1}{2.103}+...+\frac{1}{299.400}}\)
Cho: A= \(\frac{1}{1.300}+\frac{1}{2.301}+\frac{1}{3.302}+...+\frac{1}{101.400}\)
Chứng minh rằng:
\(A=\frac{1}{299}\)(\(1+\frac{1}{2}+...+\frac{1}{101}-\frac{1}{300}+\frac{1}{301}+...+\frac{1}{400}\))
Tính:
A=\(\frac{\frac{1}{1.300}+\frac{1}{2.301}+\frac{1}{3.302}+...+\frac{1}{101.400}}{\frac{1}{1.102}+\frac{1}{2.103}+\frac{1}{3.104}+...+\frac{1}{299.400}}\)
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