1.3.5.7....99
51.52.53...99.100
Những câu hỏi liên quan
RÚT GỌN PHÂN SỐ\(\dfrac{1.3.5.7.....97.99}{51.52.53.....99.100}\)
Chứng minh \(\frac{1}{1.3}+\frac{1}{1.3.5}+\frac{1}{1.3.5.7}+...+\frac{1}{1.3.5.7...\left(2n+1\right)}< \frac{1}{2}\)
\(VT< \frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{\left(2n-1\right)\left(2n+1\right)}\)
\(2.VT< \frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{\left(2n+1\right)-\left(2n-1\right)}{\left(2n-1\right).\left(2n+1\right)}\)
\(2.VT< 1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2n-1}-\frac{1}{2n+1}\)
\(2.VT< 1-\frac{1}{2n+1}\Rightarrow VT< \frac{1}{2}-\frac{1}{2\left(2n+1\right)}< \frac{1}{2}\)
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Không làm phép tính, xét xem tổng (hiệu) sau có chia hết cho 5 không? Vì sao?
a) 2.3.5.7 + 114;
b) 2.3.5.7 - 115;
c) 1.3.5.7. 9.11 + 41;
d) 1.3.5.7. 9.11- 40
1.3.5.7.......13-30
1.3.5.7....49 bằng bao nhiêu
(2.4.6.8.....98)+(1.3.5.7....99)
Tính nhanh 1.3.5.7.....97.99
CMR:
1.3.5.7.....19=11/2.12/2.13/2.....20.2
Lời giải:
\(\frac{11}{2}.\frac{12}{2}.\frac{13}{2}....\frac{20}{2}=\frac{(12.14.16.18.20)(11.13.15.17.19)}{2^{10}}\)
\(=\frac{12}{2^2}.\frac{14}{2}.\frac{16}{2^4}.\frac{18}{2}.\frac{20}{2^2}(11.13.15.17.19)\)
\(=3.7.1.9.5.11.13.15.17.19=1.3.5.7.9.11.13.15.17.19\)
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Chứng minh: 101.102.103. ..... .200chia hết cho 1.3.5.7...... .199