1-1/2=1/2 

1-1/3=2/3

......1-1/20= 19/20 

B =1/2.2/3.3/4.4/5.....19/20

rut gon ta co B 1/20 

nho k cho em nha

=1/2×2/3×3/4×....×49/50

=(1×2×3×4×...×49)/(2×3×4×...×50)

=1/50

Chắc chắn đúng

B=(2/2-1/2).(3/3-1/3)...(50/50-1/50)

B=1/2.2/3...49/50

B=1.2.3...49/2.3...50 ;B=1/50

chắc chắn thôi ak

Bài làm

\(B=\frac{16-\left(x+1\right)^2}{x^2+10x+25}\)

\(B=\frac{\left(4-x-1\right)\left(4+x+1\right)}{\left(x+5\right)^2}\)

\(B=\frac{\left(3-x\right)\left(x+5\right)}{\left(x+5\right)^2}\)

\(B=\frac{3-x}{x+5}\)

# Học tốt #

=1x2x3x...x19/2x3x...x20

=1/20

\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)

\(B=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}...\frac{19}{20}\)

\(B=\frac{1.2.3...19}{2.3.4...20}=\frac{1.\left(2.3.4...19\right)}{\left(2.3.4...19\right).20}=\frac{1}{20}\)

\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{2}{3}\right).\left(1-\frac{3}{4}\right).....\left(1-\frac{19}{20}\right)\)

\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{19}{20}\)

Ta thấy hai phân số liên tiếp nhau, mẫu phân số thứ nhất giống với tử phân số thứ hai nên ta sẽ rút gọn chúng.

\(\Rightarrow B=\frac{1}{20}\)

B=(1-\(\frac{1}{2}\))*(1-\(\frac{1}{3}\))*(1-\(\frac{1}{4}\))*....*(1-\(\frac{1}{20}\))

  =\(\frac{1}{2}\)*\(\frac{2}{3}\)*\(\frac{3}{4}\)*.....*\(\frac{19}{20}\)

  =\(\frac{1\cdot2\cdot3\cdot4\cdot...\cdot19}{2\cdot3\cdot4\cdot...\cdot20}\)

   =\(\frac{1\cdot\left(2\cdot3\cdot4\cdot...\cdot19\right)}{\left(2\cdot3\cdot4\cdot...\cdot19\right)\cdot20}\)

   =\(\frac{1}{20}\)

\(B=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)

\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{19}{20}\)

\(B=\frac{1.2.3...19}{2.3.4...20}\)

\(B=\frac{1}{20}\)

\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)

\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{19}{20}\)

\(B=\frac{1.2.3...19}{2.3.4...20}\)

\(B=\frac{1.\left(2.3.4...19\right)}{\left(2.3.4...19\right).20}\)

\(B=\frac{1}{20}.\)

Mong mn giúp đỡ

B=( 1-1/2) (1-1/3).(1-1/4)....(1-1/20)

B=\(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times....\times\frac{19}{20}\)

\(B=\frac{1\cdot2\cdot3\cdot...\cdot19}{2\cdot3\cdot4\cdot...\cdot20}\)

\(B=\frac{1}{20}\)

A=1/3-1/3^2+...-1/3^20

=>3A=1-1/3+...-1/3^19

=>4A=1-1/3^20

=>\(A=\dfrac{3^{20}-1}{3^{20}\cdot4}\)