a) Chứng minh: \(\frac{1}{x}-\frac{1}{x+1}=\frac{1}{x\left(x+1\right)}\)
b). Tính nhẩm tổng sau: \(\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+4\right)}+\frac{1}{\left(x+4\right)\left(x+5\right)}+\frac{1}{x+5}\)
a) chứng minh: \(\frac{1}{x}-\frac{1}{x+1}=\frac{1}{x\left(x+1\right)}\)
b) tính nhẩm tổng sau:
\(\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+4\right)}+\frac{1}{\left(x+4\right)\left(x+5\right)}+\frac{1}{x+5}\)
a) Chứng minh: \(\frac{1}{x}-\frac{1}{x+1}=\frac{1}{x\left(x+1\right)}\)
b) Đố: Đố bạn tính nhẩm được tổng sau:
\(\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+4\right)}+\frac{1}{\left(x+4\right)\left(x+5\right)}+\frac{1}{x+5}\)
Tính nhanh tổng sau:
\(\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+4\right)}+\frac{1}{\left(x+4\right)\left(x+5\right)}+\frac{1}{\left(x+5\right)\left(x+6\right)}=\)
tính nhanh tổng sau
\(\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+2\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+4\right)}\)
\(+\frac{1}{\left(x+4\right)\left(x+5\right)}+\frac{1}{\left(x+5\right)\left(x+6\right)}\)
Tính A = \(\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{2}{\left(x+3\right)\left(x+4\right)}+\frac{4}{\left(x+4\right)\left(x+5\right)}+\frac{8}{\left(x+5\right)\left(x+6\right)}\)
Tính Q :
\(Q=\frac{1}{\left(x-2\right)\left(x-3\right)}+\frac{1}{\left(x-3\right)\left(x-4\right)}+\frac{1}{\left(x-4\right)\left(x-5\right)}+\frac{1}{\left(x-5\right)\left(x-6\right)}..\)
Cho \(A=\frac{1}{\left(x+y\right)^3}\left(\frac{1}{x^4}-\frac{1}{y^4}\right);B=\frac{1}{\left(x+y\right)^4}\left(\frac{1}{x^3}-\frac{1}{y^3}\right);C=\frac{1}{\left(x+y\right)^5}\left(\frac{1}{x^2}-\frac{1}{y^2}\right)\)
a) Rút gọn tổng A+B+C
b) Tính tổng A+B+C tại x=2016;y=2017
Tinh nhanh tong sau:\(\frac{1}{x\left(x+1\right)}\)+\(\frac{1}{\left(x+1\right)\left(x+2\right)}\)+\(\frac{1}{\left(x+2\right)\left(x+3\right)}\)+\(\frac{1}{\left(x+3\right)\left(x+4\right)}\)+\(\frac{1}{\left(x+4\right)\left(x+5\right)}\)+\(\frac{1}{\left(x+5\right)\left(x+6\right)}\)
Đố các bn tính được tổng sau:
\(\frac{1}{x\left(x+1\right)}\)+ \(\frac{1}{\left(x+1\right)\left(x+2\right)}\)+\(\frac{1}{\left(x+2\right)\left(x+3\right)}\)+\(\frac{1}{\left(x+3\right)\left(x+4\right)}\)+\(\frac{1}{\left(x+4\right)\left(x+5\right)}\)+\(\frac{1}{\left(x+5\right)\left(x+6\right)}\)
Ai nhanh mk tick
