Đặt \(A=\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)........\left(1+\frac{1}{2009}\right)\)
\(\Rightarrow A=\frac{2+1}{2}.\frac{3+1}{3}.\frac{4+1}{4}........\frac{2009+1}{2009}\)
\(\Rightarrow A=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}..............\frac{2010}{2009}\)
\(\Rightarrow A=\frac{3.4.5............2010}{2.3.4..........2009}=\frac{2010}{2}=1005\)
Vậy A=1005
Chúc bn học tốt
Giá trị biểu thức \(A=\dfrac{2008+\dfrac{2007}{2}+\dfrac{2006}{3}+\dfrac{2005}{4}+...+\dfrac{2}{2007}+\dfrac{1}{2008}}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+...+\dfrac{1}{2008}+\dfrac{1}{2009}}\) là \(A=........\)
Tính:
B = \(\dfrac{1+2+2^2+2^3+...+2^{2008}}{1-2^{2009}}\)
Tính
a, A= \(\left(\frac{3}{5}\right)^2.5^2-\left(2\frac{1}{4}\right)^3:\left(\frac{3}{4}\right)^3+\frac{1}{2}\)
b, B= \(\left[\frac{4}{11}.\left(\frac{1}{25}\right)^0+\frac{7}{22}.2\right]^{2010}-\left(\frac{1}{2^2}:\frac{8^2}{4^4}\right)^{2009}\)
Giải hộ bài này giúp mik nhé
Bài 1 : viết gọn các biểu thức sau :
A= 3+32+33+...+349+350
B= 2-22+23-24+...+22009-22010
C= \(\frac{1}{1.2}\) + \(\frac{1}{2.3}\) + \(\frac{1}{3.4}\) + ... + \(\frac{1}{2008.2009}\)
D= \(\frac{1}{3}\) + \(\frac{1}{15}\) + \(\frac{1}{35}\) + \(\frac{1}{63}\) + \(\frac{1}{99}\)
Tính tổng sau: a) 1/2+1/6+1/12+1/20+1/30 b) 1/15+1/35+1/63+1/99+1/143 c) 1/6+1/12+1/20+1/30+1/42+1/56 d) 1/2+1/2^2+1/2^3+1/2^4+1/2^5 e) 1/7+1/7^2+1/7^3+...+1/7^100 f) 1+1/2*(1+2)+1/3*(1+2+3)+1/4*(1+2+3+4)+...+1/200*(1+2+3+..+200) g) (1/2+1)*(1/3+1)*(1/4+1)*..*(1/100+1) h) (1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/2022) Giúp mk vs ạkkk
Tính
A= 1+1/2(1+2)+1/3(1+2+3)+1/4(1+2+3+4)+...+1/20(1+2+3+...+20)
Chứng minh \(\dfrac{1}{1+2+3}\)+\(\dfrac{1}{1+2+3+4}\)+......+\(\dfrac{1}{1+2+3+4+...+59}\)<\(\dfrac{2}{3}\)
So sánh 2 biểu thức sau:
\(A=\frac{5^{2010}+1}{5^{2011}+1}\)và\(B\frac{5^{2009}+1}{5^{2010}+1}\)
Tính nhanh :
\(\dfrac{\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}}{\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}\right)-\dfrac{1}{2}.\dfrac{1}{3}.\dfrac{1}{4}}\)