Question

tinh gia tri cua bieu thuc sau :

A=1/199-1/199.198-1/198.197-1/197.196-.............-1/3.2-1/2.1

Answer 1

Ta có : \(A=\dfrac{1}{199}-\dfrac{1}{199.198}-\dfrac{1}{198.197}-\dfrac{1}{197.196}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)

\(=\dfrac{1}{199}-\left(\dfrac{1}{199.198}+\dfrac{1}{198.197}+\dfrac{1}{197.196}+...+\dfrac{1}{3.2}+\dfrac{1}{2.1}\right)\)

\(=\dfrac{1}{199}-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{196.197}+\dfrac{1}{197.198}+\dfrac{1}{198.199}\right)\)

\(=\dfrac{1}{199}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...-\dfrac{1}{198}+\dfrac{1}{198}-\dfrac{1}{199}\right)\)

\(=\dfrac{1}{199}-\left(1-\dfrac{1}{199}\right)\)

\(=\dfrac{1}{199}-\dfrac{198}{199}=\dfrac{-197}{199}\)

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