1/2^2=4
1/3^2<1/2.3
.................
1/100^2<1/99.100
A<1/4+1/2.3+...+1/99.100
A<1/4+1/2-1/100
A<1/4<3/4
Vậy A<3/4(dpcm).CHÚC BẠN HỌC TỐT!
a, Chứng tỏ rằng: \(\dfrac{12n+1}{30n+2}\) là phân số tối giản.
b, Chứng minh rằng: \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{100^2}< 1\)
Chứng minh rằng \(\dfrac{1}{3^2}+\dfrac{1}{4^2}+\dfrac{1}{5^2}+...+\dfrac{1}{100^2}< \dfrac{1}{2}\)
Cho A= \(\dfrac{1}{4^2}+\dfrac{1}{6^2}+\dfrac{1}{8^2}+\dfrac{1}{10^2}+...+\dfrac{1}{160^2}\)
Chứng minh: \(\dfrac{1}{8}< A< \dfrac{3}{16}\)
CMR: \(\dfrac{200-\left(3+\dfrac{2}{3}+\dfrac{2}{4}+\dfrac{2}{5}+...+\dfrac{2}{100}\right)}{\dfrac{1}{2}+\dfrac{2}{3}+\dfrac{3}{4}+...+\dfrac{99}{100}}=2\)
Helppp!!!
tính
a) (\(2\dfrac{5}{6}+1\dfrac{4}{9}\)):(\(10\dfrac{1}{12}\)-9\(\dfrac{1}{2}\))
b) \(\dfrac{0,8:\left(\dfrac{4}{5}:1,25\right)}{0,64-\dfrac{1}{25}}\)
c) \(\dfrac{\left(100-\dfrac{2}{25}\right):\dfrac{4}{7}}{\left(6\dfrac{5}{9}-3\dfrac{1}{4}\right).2\dfrac{2}{27}}\) + (1,2 . 0,5) : \(\dfrac{3}{5}\)
Tìm y:
-y:\(\dfrac{1}{2}\)-\(\dfrac{5}{2}\)=4\(\dfrac{1}{2}\)
Tính:
N = \(\dfrac{3}{4}\).\(\dfrac{8}{9}\).\(\dfrac{15}{16}\)....\(\dfrac{899}{900}\).\(\dfrac{960}{961}\)
S=\(\dfrac{1}{1.2.3}\)+\(\dfrac{1}{2.3.4}\)+\(\dfrac{1}{3.4.5}\)+...+\(\dfrac{1}{10.11.12}\)+\(\dfrac{1}{11.12.13}\)
Tính :
a) \(\dfrac{1}{3}+\dfrac{3}{8}-\dfrac{7}{12}\)
b) \(\dfrac{-3}{14}+\dfrac{5}{8}-\dfrac{1}{2}\)
c) \(\dfrac{1}{4}-\dfrac{2}{3}-\dfrac{11}{18}\)
d) \(\dfrac{1}{4}+\dfrac{5}{12}-\dfrac{1}{13}-\dfrac{7}{8}\)
Thực hiện phép tính( tính nhanh nếu có thể)
a, \(\left(-\dfrac{1}{2}\right)^2.\dfrac{7}{4}:\left(\dfrac{5}{8}-1\dfrac{3}{16}\right)\)
b, \(17\dfrac{6}{11}.\dfrac{4}{27}-8\dfrac{6}{11}:\dfrac{27}{4}+350\%\)
a, \(\dfrac{x-2}{15}+\dfrac{x-3}{14}+\dfrac{x-4}{13}+\dfrac{x-5}{12}=4\)
b, \(\dfrac{x+1}{19}+\dfrac{x+2}{18}+\dfrac{x+3}{17}+...+\dfrac{x+18}{2}+18=0\)
Cảm ơn khi đã giúp mình
