vì\(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}=\frac{3}{6}-\frac{2}{6}-\frac{1}{6}=\frac{3-2-1}{6}=\frac{0}{6}=0\)
=> \(\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right)\cdot\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)=\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right)\cdot0=0\)
a) Chứng minh rằng:
1-\(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{199}-\frac{1}{200}=\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}\)
b) Giải bài toán trên trong trường hợp tổng quát.
1.CMR:
\(\frac{1}{101}+\frac{1}{102}+..+\frac{1}{199}+\frac{1}{200}< 1\)
\(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{32}>3\)
1.CMR:
\(\frac{1}{101}+\frac{1}{102}+..+\frac{1}{199}+\frac{1}{200}< 1\)
\(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{32}>3\)
Bài 1:
\(A=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{99}.\)Chứng minh rằng \(A⋮100\)
\(A=\frac{1}{11}+\frac{1}{12}+\frac{2}{13}+...+\frac{1}{70}.\)Chứng minh rằng \(A>\frac{4}{3}\)
Bài 2:Tính \(\frac{A}{B}\)
\(A=\frac{1}{2}+\frac{1}{3}+...+\frac{1}{200}\) ;\(B=\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{198}{2}+\frac{199}{1}\)
\(A=\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{9.10}\) ;\(B=\frac{1}{6.10}+\frac{1}{7.9}+\frac{1}{8.8}+\frac{1}{9.7}+\frac{1}{10.6}\)
giúp mk với các nhà toán thông thái à!
Ai hộ mình bài này với ,cảm ơn trước nhé
Dạng tìm tỉ số:Tính \(\frac{A}{B}\) biết rằng:
\(A=\frac{1}{2}+\frac{1}{3}+...+\frac{1}{200};\) \(B=\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{198}{2}+\frac{199}{1}\)
\(A=\frac{1}{1\cdot2}+\frac{1}{3\cdot4}+...+\frac{1}{9\cdot10};\) \(B=\frac{1}{6\cdot10}+\frac{1}{7\cdot9}+\frac{1}{8\cdot8}+\frac{1}{9\cdot7}+\frac{1}{10\cdot6}\)
Dấu * là nhân nha (Đừng nhầm với dấu ... nhé)
\(a,1\frac{13}{15}.0,75-\left(\frac{8}{15}+0,25\right).\frac{24}{47}\)
\(b,5:\left(4\frac{3}{4}-1\frac{25}{28}\right)-1\frac{3}{8}:\left(\frac{3}{8}+\frac{9}{20}\right)\)
\(c,6\frac{5}{12}:2\frac{3}{4}+11\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{5}\right)\)
\(d,\left(\frac{3}{5}+0,415-\frac{3}{200}\right).2\frac{2}{3}.0,25\)
\(e,\left(\frac{3}{8}+\frac{-3}{4}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)
\(g,1\frac{13}{15}.0,75-\left(\frac{11}{20}+25\%\right);\frac{7}{3}\)
1.thực hiện phép tính
a.\(\frac{-1}{12}-\left(2^5_8-\frac{1}{3}\right)\)
b.-1,75-\(\left(\frac{-1}{9}-2^1_{18}\right)\)
c.\(\frac{2}{5}+\frac{-4}{3}+\frac{-1}{2}\)
d.\(\frac{3}{12}-\left(\frac{6}{15}-\frac{3}{10}\right)\)
e.\(\left(8^5_{11}+3^5_8\right)-3^5_{11}\)
f.\(\frac{4}{9}:\left(\frac{-1}{7}\right)+6^5_9:\left(\frac{-1}{7}\right)\)
g.\(\frac{-1}{4}.13^9_{11}-0,25.6^2_{11}\)
h.\(5^{27}_5+\frac{27}{23}+0,5-\frac{5}{27}+\frac{16}{23}\)
i.\(\frac{3}{8}.27^1_5-51^1_5.\frac{3}{8}+19\)
a) Chứng minh: \(\frac{11}{15}< \frac{1}{21}+\frac{1}{22}+\frac{1}{23}+...+\frac{1}{60}< \frac{3}{2}\)
b) Chứng minh: \(3< 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{63}< 6\)
tìm x:
\(a,\frac{x}{2}+\frac{2x}{3}+\frac{x+1}{4}+\frac{2x+1}{6}=\frac{8}{3}\)
\(b,\frac{3}{2x+1}+\frac{10}{4x+2}-\frac{6}{6x-3}=\frac{12}{26}\)
