Question

Vă rog !!! Punctul C de la ex 20

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

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

1/44*45 = 1/44 - 1/45

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1/1*2 + 1/2*3 + 1/3*4 + ...+ 1/44*45 = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/44 - 1/45 = 1 - 1/45 = 45/45 - 1/45 = 44/45

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1/45*45 = 1/45 - 1/46

1/46*47 = 1/46 - 1/47

1/47*48 = 1/47 - 1/48

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

1/89*90 = 1/89 - 1/90

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1/45*45 + 1/46*47 + 1/47*48 + ...+ 1/89*90 = 1/45 - 1/46 + 1/46 - 1/47 + 1/47 - 1/48 + ... + 1/89 - 1/90 = 1/45 - 1/90 = 2/90 - 1/90 = 1/90

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44/45 - 1/90 = 88/90 - 1/90 = 87/90

120/29*87/90 = 4

√4 = 2