Tính ( bằng cách hợp lý nếu có thể ):
a) 1/2.3 +1/3.4 + 1/4.5 + .... + 1/9.10
b) 1/2 + 1/6 + 1/12 + .... +1/90
c) 12/1.2 . 22/2.3 . 32/3.4 . 42/4.5
1-\(\dfrac{1}{1.2}\)-\(\dfrac{1}{2.3}\)-...-\(\dfrac{1}{9.10}\)<\(\dfrac{1}{9}\)
Tìm x :
\(\dfrac{1}{1.2}.\left|2x-1\right|+\dfrac{1}{2.3}.\left|2x-1\right|+\dfrac{1}{3.4}+..+\dfrac{1}{1996.1997}.\left|2x-1\right|=1996\)
Tính :
\(\dfrac{1.2+2.3+3.4+...+20.21}{1+2-3-4+5+6-7-8+...+197+198-199-200+201}\)
So sánh M = \(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+.......+\(\dfrac{1}{49.50}\) với 1
Tính nhanh
E = \(\dfrac{-9}{10}.\dfrac{5}{14}+\dfrac{1}{10}.\dfrac{-9}{2}+\dfrac{1}{7}.\dfrac{-9}{10}\)
Chứng tỏ rằng: \(\dfrac{1}{1.2}+\dfrac{1}{2.3}\text{+}\dfrac{1}{3.4}\text{+}.........\text{+}\dfrac{1}{99.100}\)< 1
Mau nha
100/111 của C,biết C bằng 1.2 nhân 4 cộng 1/4 nhân 6 cộng ... cộng 1/1998 nhân 2000
a) \(\dfrac{2}{1^2}.\dfrac{6}{2^2}.\dfrac{12}{3^2}.\dfrac{20}{4^2}.\dfrac{30}{5^2}.....\dfrac{110}{10^2}.x=-20\)
b) \(\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2013}\right).x+2013=\dfrac{2014}{1}+\dfrac{2015}{2}+...+\dfrac{4025}{2012}+\dfrac{4026}{2013}\)
c) \(\left(\dfrac{1}{1.2}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\right).x=\dfrac{2012}{51}+\dfrac{2012}{52}+...+\dfrac{2012}{99}+\dfrac{2012}{100}\)