Tìm S biết S=50+50/3+25/3+20/4+10/3+100/6.7+....+100/98.99+1/99
Chứng tỏ:\(\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+...+\frac{1}{49}+\frac{1}{50}=\frac{99}{50}-\frac{97}{45}+...+\frac{7}{4}-\frac{5}{3}=1\)
Chứng minh :
a) \(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}< \frac{3}{16}\) \(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{4^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}< \frac{3}{16}\)
b)\(\frac{1}{41}+\frac{1}{42}+\frac{1}{43}+...+\frac{1}{79}+\frac{1}{80}< \frac{7}{12}\)
c) Cho \(S=\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}\)
Chứng minh \(1< S< 2\)
Tính giá trị của biểu thức, tính nhanh nếu có thể
9) \(\frac{13}{50}\) + 9% + \(\frac{41}{100}\) + 24%
10) 2011,2012 . 2000 ( \(\frac{5}{6}\) - \(\frac{1}{3}\) - 50% ) . 1,234 + 10
11) \(\frac{120-0,5.40.5.0,2.20.0,25-20}{1+5+9+........+33+37}\)
12) \(6\frac{2}{7}+7\frac{3}{5}+8\frac{6}{9}+9\frac{1}{4}+\frac{2}{5}+\frac{5}{7}+\frac{1}{3}+\frac{3}{4}+1997\)
Tính D biết : \(D=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{\frac{99}{1}+\frac{98}{2}+\frac{97}{3}+...+\frac{1}{99}}\)
Tính :
a ) \(\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right)...\left(\frac{1}{99}+1\right)\)
b )\(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right)...\left(\frac{1}{100}-1\right)\)
c ) \(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{899}{30^2}\)
1. Tính hợp lý :
A = \(\frac{\left(1+2+3+...+100\right)x\left(101x102-101x101-50-51\right)}{2+4+8+16...+2048}\)
B = \(\frac{101+100+99+...+3+2+1}{101-100+99-98+...+3-2+1}\)
2. Tìm số tự nhiên x, biết :
a, 697 : \(\frac{15x+364}{x}\)=17
b, 92.4 - 27 = \(\frac{x+350}{x}\)+315
c, 720 : [ 41 - ( 2x -5)] = 40
d, (x+1) + (x+2) +...+ (x+100) = 5750
Chứng minh rằng :
\(100-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)=\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{99}{100}\)
Bài 4: THực hiện phép tính một cách hợp lý:
a) \(\frac{7}{19}.\frac{8}{11}+\frac{3}{11}.\frac{7}{19}+\frac{-12}{19}\) b) \(\frac{-7}{25}.\frac{39}{-14}.\frac{50}{78}\) c) \(\left(\frac{3}{8}+\frac{-3}{4}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)
