Question

Va rog urgent aceste exercitii...


1/1·2 + 1/2·3 + ...... + 1/2022·2023

1/1+√2 + 1/√2+√3 + 1/√3+√4 + ...... + 1/√8+√9

(√5-√4)(√3+√2)(√5+√4)(√2-√2)

Answer 1

Răspuns:

$\frac{1}{1*2} + \frac{1}{2*3} + ... + \frac{1}{2022*2023} =\\\\\frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + ... + \frac{1}{2022} - \frac{1}{2023} = \\\\1 - \frac{1}{2023} = \frac{2023-1}{2023} = \frac{2022}{2023}$

(√5-√4)(√3+√2)(√5+√4)(√2-√2) = (√5-√4)(√3+√2)(√5+√4)*0 = 0

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