1. Có 1 thừa số là \(1-\frac{5}{5}=0\) nên tích sẽ bằng 0

2.\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.......\frac{49}{50}=\frac{1}{50}\)

=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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\cdot\cdot\left(1-\frac{1}{20}\right)\)

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

\(=\frac{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot\cdot\cdot\cdot19}{2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot\cdot\cdot20}\)

\(=\frac{1\cdot\left(2\cdot3\cdot4\cdot5\cdot\cdot\cdot19\right)}{\left(2\cdot3\cdot4\cdot5\cdot\cdot\cdot19\right)\cdot20}\)

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

a,B=1/2^2+1/3^2+...+1/8^2

suy ra B=1/2.2+1/3.3+1/4.4+....+1/8.8

mà 1/2.2<1/1.2;1/3.3<1/2.3;...;1/8.8<1/7.8

suy ra B<1/1.2+1/2.3+...+1/7.8

B<1-1/2+1/2-1/3+1/3-1/4+...+1/7-1/8

B<1-1/8<1 suy ra B <1 

b,C=(1-1/2).(1-1/3)....(1-1/20)

C=1/2.2/3....19/20

C=1.2.3....18.19/2.3.4...19.20

C=1/20

(mình ko chắc vs hết quả phần b đâu nha)