Ta có: H=(1/2+1/3+1/4)+(1/5+...+1/8)+(1/9+1/16)+(1/17+...+1/63)
=> H=13/12 + (1/5+...+1/8)+(1/9+...+1/16)+(1/17+...+1/63)
=> H> 1 + 4x(1/8) + 8x (1/16) + (1/17+...+1/63)
=> H> 1+ 1/2 + 1/2 + (1/17+...+1/63)
=> H> 1+1+(1/17+...+1/63)
=> H>1+1
=> H>2
Chứng minh rằng:
\(A=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.......+\frac{1}{63}\)
Chứng minh rằng: \(A< 6\)
Chứng minh rằng:
a) \(A=1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+.........+\frac{1}{100^2}< 2\)
b) \(B=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.........+\frac{1}{63}< 6\)
1)Chứng minh các phân số sau là các phân số tối giản:
a)\(A=\frac{12n+1}{30n+2}\)
b)\(B=\frac{14n+17}{21n+25}\)
2)Chứng minh rằng:
a)\(A=1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< 2\)
b)\(B=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{63}< 6\)
c)\(C=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.....\frac{9999}{10000}< \frac{1}{100}\)
Chứng minh rằng
a) \(A=1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}<2\)
b)\(B=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{63}<6\)
cho:
a) A= 2+\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{62}+\frac{1}{63}+\frac{1}{64}+\frac{1}{65}+\frac{1}{66}+\frac{1}{67}\)
chứng minh rằng A>5
b) B= \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{89^2}+\frac{1}{90^2}\)
chứng minh rằng \(\frac{40}{91}\)<B<1
Chứng minh rằng:
\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{63}>2\)
Chứng minh rằng:
\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{63}>2\)
Chứng minh \(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{63}+\frac{1}{64}>4\)
Bài 1 : Chứng minh
a) \(A=1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< 2\)
b) \(B=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{63}< 6\)
c) \(C=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}...\frac{9999}{10000}< \frac{1}{100}\)
