Cho B = \(\dfrac{1}{1.2}\)+\(\dfrac{1}{3.4}\)+\(\dfrac{1}{4.5}\)+ ... + \(\dfrac{1}{99.100}\)
Chứng minh \(\dfrac{7}{12}\)<B<\(\dfrac{5}{6}\)
Tính giá trị biểu thức
\(A=\dfrac{1}{1.2}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)
\(x-\dfrac{1}{1.2}-\dfrac{1}{2.3}-\dfrac{1}{3.4}-...-\dfrac{1}{98.99}=\dfrac{1}{100}+\dfrac{1}{99.100}\)
Thực hiện phép tính:
\(A=3.\dfrac{1}{1.2}-5.\dfrac{1}{2.3}+7.\dfrac{1}{3.4}-...+15.\dfrac{1}{7.8}-17.\dfrac{1}{8.9}\)
Chứng minh rằng:
\(\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{49.50}=\dfrac{1}{26}+\dfrac{1}{27}+...+\dfrac{1}{50}\)
1, Tính hợp lí
\(A=\dfrac{0.5+\dfrac{7}{12}-\dfrac{5}{6}}{1-\dfrac{2}{3}+0,75}\)
\(B=-66.\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{11}\right)+124.\left(-37\right)+126.\left(-62\right)\)
\(N=\left(60\dfrac{7}{13}+50\dfrac{8}{13}-11.\dfrac{2}{13}\right)x\) (Với \(x=-2017\dfrac{7}{10}\))
\(M=\left(1-\dfrac{2}{2.3}\right).\left(1-\dfrac{2}{3.4}\right).\left(1-\dfrac{2}{4.5}\right).....\left(1-\dfrac{2}{99.100}\right)\)
Tính tổng sau: \(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{999.1000}\)
Tính: a) A=\(\dfrac{1}{2}\)+\(\dfrac{1}{2^2}\)+\(\dfrac{1}{2^3}\)+...+\(\dfrac{1}{2^{100}}\)
b) \(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+\(\dfrac{1}{3.4}\)+...+\(\dfrac{1}{2023.2024}\)
cứu tôi mng owiiii :((
Tính:
a) \(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) +...+ \(\dfrac{1}{1999.2000}\)
b) \(\dfrac{1}{1.4}\) + \(\dfrac{1}{4.7}\) + \(\dfrac{1}{7.10}\) +...+ \(\dfrac{1}{100+103}\)
c) \(\dfrac{8}{9}\) - \(\dfrac{1}{72}\) - \(\dfrac{1}{56}\) - \(\dfrac{1}{42}\) -...-\(\dfrac{1}{6}\) - \(\dfrac{1}{2}\)
Cho biểu thức A=\(\dfrac{1}{2^2}\)+\(\dfrac{1}{3^2}\)+\(\dfrac{1}{4^2}\)+\(\dfrac{1}{5^2}\)+\(\dfrac{1}{6^2}\)+\(\dfrac{1}{7^2}\)+\(\dfrac{1}{8^2}\)+\(\dfrac{1}{9^2}\)+\(\dfrac{1}{10^2}\)
Chứng minh rằng A<1
