Question

Tính :

\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+......+\dfrac{1}{49.50}\)

Answer 1

\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{49.50}\)

\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\)

\(A=1-\dfrac{1}{50}\)

\(A=\dfrac{49}{50}\)

Answer 2

\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{49.50}\)

\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\)

\(A=1-\dfrac{1}{50}=\dfrac{49}{50}\)

Answer 3

\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+.....+\dfrac{1}{49.50}.\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+.....+\dfrac{1}{49}-\dfrac{1}{50}.\)

\(=\left(-\dfrac{1}{2}+\dfrac{1}{2}\right)+\left(-\dfrac{1}{3}+\dfrac{1}{3}\right)+.....+\left(-\dfrac{1}{49}+\dfrac{1}{49}\right)+\left(1-\dfrac{1}{50}\right).\)\(=0+0+0+.....+0+\left(1-\dfrac{1}{50}\right).\)

\(=1-\dfrac{1}{50}.\)

=\(\dfrac{49}{50}.\)

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Answer 4

\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\)

\(A=1-\dfrac{1}{50}\)

\(A=\dfrac{49}{50}\)