lớn hơn vì ta có thể thấy: các số như 1/2,3/4,5/6 đã lớn hơn 0,01
khi ta X len ta se duoc ket qua > 0,01
duyet minh nha
1/2 X 3/4 X 5/6 X .....X 9999/10000 > 0,01
tính các tích sau
\(a=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{9999}{10000}\)
\(b=\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times...\times\left(1-\frac{1}{10000}\right)\)
\(c=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times...\times\left(1-\frac{1}{1994}\right)\)
\(d=\left(1+\frac{1}{1\times3}\right)\times\left(1+\frac{1}{2\times4}\right)\times\left(1+\frac{1}{3\times5}\right)\times...\times\left(1+\frac{1}{99\times100}\right)\)
cho A=\(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\) .......\(\times\)\(\frac{9999}{10000}\).khi do 200\(\times\)A=...........
Cho \(A=\left(\frac{1}{2^2}-1\right)\times\left(\frac{1}{3^2}-1\right)\times\left(\frac{1}{4^2}-1\right)\times...\times\left(\frac{1}{100^2}-1\right)\)
So sánh A với \(-\frac{1}{2}\)
1/tìm STN nhỏ nhất chia cho 5 dư 1,chia7 dư 5 2/CMR:\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{199}-\frac{1}{200}=\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}\) 3/CMR:\(\frac{51}{2}\times\frac{52}{2}\times...\times\frac{100}{2}=1\times3\times5\times...\times97\times99\) 4/cho A=\(\frac{1}{2}\times\frac{3}{4}\times\frac{5}{6}\times...\times\frac{9999}{10000}\) so sánh A với 0,01 5/CMR:\(\left(1+2+3+...+n\right)-7\) chia hết cho 10
Cho : A = \(\frac{1}{4}\)\(\times\)\(\frac{3}{6}\)\(\times\)\(\frac{5}{8}\)\(\times\).......\(\times\)\(\frac{43}{46}\)
B=\(\frac{3}{5}\)\(\times\)\(\frac{4}{7}\)\(\times\)..........\(\times\)\(\frac{44}{47}\)
a) so sánh A với B
b) chứng minh A<\(\frac{1}{133}\)
Cho \(A=\frac{1}{2}\times\frac{3}{4}\times\frac{5}{6}\times...\times\frac{199}{200}\)và chứng minh \(A^2< \frac{1}{201}\)
\(\frac{1}{3}\times\frac{2}{5}\times\frac{3}{7}\times\frac{4}{9}\times\frac{5}{11}\times\frac{6}{15}\times\frac{7}{15}\times\frac{8}{15}\times\frac{9}{19}\times\frac{10}{21}\times\frac{11}{32}\times\frac{12}{25}\times\left\{\frac{126}{252}-\frac{2}{4}\right\}\)
tính:
\(A=\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times...\times\left(1-\frac{1}{9801}\right)\times\left(1-\frac{1}{10000}\right)\)
