Tính:

(121):(131):(141):\left(\dfrac{1}{2}-1\right):\left(\dfrac{1}{3}-1\right):\left(\dfrac{1}{4}-1\right): ... : (1501)\left(\dfrac{1}{50}-1\right)

Chứng minh rằng:

(1+13+15+...+150)(12+14+16+...+1100+1102)=152+153+...+1100+1101+1102\left(1+\dfrac{1}{3}+\dfrac{1}{5}+...+\dfrac{1}{50}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{6}+...+\dfrac{1}{100}+\dfrac{1}{102}\right)=\dfrac{1}{52}+\dfrac{1}{53}+...+\dfrac{1}{100}+\dfrac{1}{101}+\dfrac{1}{102}

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