\(A=\left(\frac{1}{16}-1\right)\left(\frac{1}{25}-1\right)\left(\frac{1}{36}-1\right)...\left(\frac{1}{100}-1\right)\)

\(-A=\left(1-\frac{1}{16}\right)\left(1-\frac{1}{25}\right)\left(1-\frac{1}{36}\right)...\left(1-\frac{1}{100}\right)\)

\(-A=\frac{15}{16}\cdot\frac{24}{25}\cdot\frac{35}{36}\cdot...\cdot\frac{99}{100}\)

\(-A=\frac{\left(3\cdot5\right)\left(4\cdot6\right)\left(5\cdot7\right)...\left(9\cdot11\right)}{\left(4\cdot4\right)\left(5\cdot5\right)\left(6\cdot6\right)...\left(10\cdot10\right)}\)

\(-A=\frac{\left(3\cdot4\cdot5\cdot...\cdot9\right)\left(5\cdot6\cdot7\cdot...\cdot11\right)}{\left(4\cdot5\cdot6\cdot...\cdot10\right)\left(4\cdot5\cdot6\cdot...\cdot10\right)}\)

\(-A=\frac{3\cdot11}{10\cdot4}=\frac{33}{40}\)

\(A=-\frac{33}{40}\)

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(x;y)=(0;0);(2;2)

Ta có x(y-2)= 3.1=1.3=-1. -3= -3. -1

Xét từng trường hợp

TH1: x=3

          y-2=1 => y=3

TH2 x=1

       y-2=3 => y=5

Bạn làm tiếp với các Th tiếp theo nhé

x,y là số nguyên => x;y-2 \(\inƯ\left(3\right)=\left\{-3;-1;1;2\right\}\)

Ta có bảng

Vậy (x;y)={(-3;1);(-1;-1);(1;5);(3;3)}