\(\frac{1.2-1}{2!}+\frac{2.3-1}{3!}+............+\frac{99.100-1}{100!}\)
\(=\frac{1.2}{2!}-\frac{1}{2!}+\frac{2.3}{3!}-\frac{1}{3!}+..........+\frac{99.100}{100!}-\frac{1}{100!}\)
\(=\left(\frac{1.2}{2!}+\frac{2.3}{3!}+.........+\frac{99.100}{100!}\right)-\left(\frac{1}{2!}+\frac{1}{3!}+.....+\frac{1}{100!}\right)\)
\(=\left(1+1+\frac{1}{2!}+.........+\frac{1}{98!}\right)-\left(\frac{1}{2!}+\frac{1}{3!}+....+\frac{1}{100!}\right)\)
\(=2-\frac{1}{99!}-\frac{1}{100!}< 2\)
bài1: Tìm x
\(\left|x+\dfrac{1}{1.2}\right|+\left|x+\dfrac{1}{2.3}\right|+......+\left|x+\dfrac{1}{99.100}\right|=100x\)
Help me, please! Thanks.
1/ Tính
\(\dfrac{\left(1+2+3+...+100\right).\left(\dfrac{1}{3}-\dfrac{1}{5}-\dfrac{1}{7}-\dfrac{1}{9}\right).\left(6,3.12-21.3,6\right)}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{100}}\)
2/ Tìm x:
\(\dfrac{x+4}{2000}+\dfrac{x+3}{2001}=\dfrac{x+2}{2002}+\dfrac{x+1}{2003}\)
3/ Cho \(A=\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+...+\dfrac{1}{99.100}\)
Chứng minh: \(\dfrac{7}{12}< A< \dfrac{5}{6}\)
4/ Tìm \(a,b\varepsilon Q:a+b=a.b=a:b\)
Giúp mik nha mai mik cần rồi.
Cho A= \(\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+...+\dfrac{1}{99.100}\) và B= \(\dfrac{2013}{51}+\dfrac{2013}{52}+\dfrac{2013}{53}+..+\dfrac{2013}{100}\)
Chứng minh rằng: \(\dfrac{B}{A}\) là một số nguyên
So sánh A và B với \(\dfrac{1}{2}\) biết :
\(A=\dfrac{1}{1.2^2}+\dfrac{1}{2.3^2}+\dfrac{1}{3.4^2}+........+\dfrac{1}{49.50^2}\) và
\(B=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+.......+\dfrac{1}{50^2}\)
\(\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+.....+\dfrac{1}{99.100}\) tính giá trị biểu thức
Tính giá trị của các biểu thức sau:
a) A = \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{299.300}\)
b) B = \(\dfrac{10^2}{16.26}+\dfrac{10^2}{26.36}+\dfrac{10^2}{36.46}+...+\dfrac{10^2}{86.96}\)
Tính tổng A=\(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+\(\dfrac{1}{3.4}\)+...+\(\dfrac{1}{49.50}\)
1. Tính:
a. \(\dfrac{-1}{4}+\dfrac{5}{6}\) b. \(\dfrac{5}{12}+\dfrac{-7}{8}\) c. \(\dfrac{-7}{6}+\dfrac{-3}{10}\) d. \(\dfrac{-3}{7}+\dfrac{5}{6}\)
2. Tính :
a. \(\dfrac{2}{14}-\dfrac{5}{2}\) b. \(\dfrac{-13}{12}-\dfrac{5}{18}\) c. \(\dfrac{-2}{5}-\dfrac{-3}{11}\) d. \(0,6--1\dfrac{2}{3}\)
3. Tính :
a. \(\dfrac{-1}{39}+\dfrac{-1}{52}\) b. \(\dfrac{-6}{9}-\dfrac{12}{16}\) c. \(\dfrac{-3}{7}-\dfrac{-2}{11}\) d.\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{8.9}+\dfrac{1}{9.10}\)
CMR : a) 1/2! + 2/3! + 3/4! +...+ 99/100! < 1
b) 1.2-1/2! + 2.3-1/3! + 3.4-1/4! +...+ 99.100-1/100! < 2
