Question

Va rog, am nevoie de ajutor

Answer 1

Răspuns:

Explicație pas cu pas:

1/1*2 = 1 - 1/2

1/2*3 = 1/2 - 1/3

1/3*4 = 1/3 - 1/4

..............

1/53*54 = 1/53 - 1/54

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1/1*2 + 1/2*3 + 1/3*4 + ... + 1/53*54 = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/53 - 1/54 = 1 - 1/54 = 54/54 - 1/54 = 53/54

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1/54*55 = 1/54 - 1/55

1/55*56 = 1/55 - 1/56

..............

1/107*108 = 1/107 - 1/108

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1/54*55 + 1/55*56 + ... + 1/107*108 = 1/54 - 1/55 + 1/55 - 1/56 + ... + 1/107 - 1/108 = 1/54 - 1/108 = 2/108 - 1/108 = 1/108

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53/54 - 1/108 = 106/108 - 1/108 = 105/108

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105/108*180/7 = 25

x = √25 = 5