Các câu hỏi tương tự
Tìm x biết:
a,\(\frac{\left|x\right|}{\left(a+3\right)\cdot\left(2-a\right)}=\frac{1}{a+3}+\frac{1}{2-a}\left(a\ne2;a\ne-3\right)\)
b,\(\frac{\left|x\right|-3}{\left(a-1\right)\cdot\left(a-2\right)}=\frac{1}{a-1}-\frac{1}{a-2}\left(a\ne1;a\ne2\right)\)
CMR
\(\frac{1}{2}\left[\frac{b-c}{\left(a-b\right)\left(a-c\right)}+\frac{c-a}{\left(b-c\right)\left(b-a\right)}+\frac{a-b}{\left(c-a\right)\left(c-b\right)}\right]=\frac{1}{a-b}+\frac{1}{b-c}+\frac{1}{c-a}\)
chứng minh :
a)
\(\frac{1}{a\left(a+1\right)}=\frac{1}{a}+\frac{1}{a+1}\)
b) \(\frac{2}{a\left(a+1\right)\left(a+2\right)}=\frac{1}{a\left(a+1\right)}-\frac{1}{a+2}\)
Thực hiện phép tính :
a, A =\(\left(1:\frac{5^2}{10^2}\right).\left(1\frac{1}{1}\right)^2+25.\left[1:\left(\frac{4}{3}\right)^2:\left(\frac{5}{4}\right)^3\right]:\left(1:\frac{-8}{27}\right)\)
b, B =\(\left(1-\frac{1}{2^2}\right).\left(1-\frac{1}{3^2}\right).\left(1-\frac{1}{4^2}\right)...\left(1-\frac{1}{100^2}\right)\)
Tính bằng cách hợp lí nhất
a) A = \(\frac{\left(1+17\right)\left(1+\frac{17}{2}\right)\left(1+\frac{17}{3}\right)...\left(1+\frac{17}{19}\right)}{\left(1+19\right)\left(1+\frac{19}{2}\right)\left(1+\frac{19}{3}\right)..\left(1+\frac{19}{17}\right)}\)
b) B = \(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)...\left(\frac{1}{99}-1\right)\left(\frac{1}{100}-1\right)\)
Bài 2a) Aleft(frac{1}{2}-1right)left(frac{1}{3}-1right)...left(frac{1}{2002}-1right)left(frac{1}{2003}-1right)b) Bleft(-1frac{1}{2^2}right)left(-1frac{1}{3^2}right)left(-1frac{1}{4^2}right)...left(-1frac{1}{2003^2}right)left(-1frac{1}{2004^2}right)c) Cleft(1-frac{1}{2^2}right)left(1-frac{1}{3^2}right)left(1-frac{1}{4^2}right)...left(1-frac{1}{n^2}right)left(nin N,nge2right)
Đọc tiếp
Bài 2
a) \(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)...\left(\frac{1}{2002}-1\right)\left(\frac{1}{2003}-1\right)\)
b) \(B=\left(-1\frac{1}{2^2}\right)\left(-1\frac{1}{3^2}\right)\left(-1\frac{1}{4^2}\right)...\left(-1\frac{1}{2003^2}\right)\left(-1\frac{1}{2004^2}\right)\)
c) \(C=\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)...\left(1-\frac{1}{n^2}\right)\left(n\in N,n\ge2\right)\)
\(A=\left(\frac{1}{1^2}-1\right)\left(\frac{1}{2^2}-1\right)\left(\frac{1}{3^2}-1\right)...\left(\frac{1}{2015^2}-1\right)\left(\frac{1}{2016^2}-1\right);B=-\frac{1}{2}\). hãy so sanh a va b
Chứng minh các đẳng thức sau: \(\frac{1}{a.\left(a+1\right)}=\frac{1}{a}-\frac{a}{a+1}\)\(\frac{2}{a.\left(a+1\right).\left(a+2\right)}=\frac{1}{a}-\frac{1}{\left(a+1\right).\left(a+2\right)}\)
Xem chi tiết
cho \(A=\left(\frac{1}{2^2}-1\right)\left(\frac{1}{3^2}-1\right)\left(\frac{1}{4^2}-1\right)...\left(\frac{1}{2016^2}-1\right)\left(\frac{1}{2017^2}-1\right)\)và b=-1/2
Hãy so sánh A với B