Question

9.Calculați:
Cu explicație, vă rog!​​

Answer 1

Răspuns:

Explicație pas cu pas:

a^2 - b^2 = (a + b)(a - b)

1 - 1/2^2 = (1 - 1/2)(1 + 1/2) = 1/2*3/2

1 - 1/3^2 = (1 - 1/3)(1 + 1/3) = 2/3*4/3

1 - 1/4^2 = (1 - 1/4)(1 + 1/4) = 3/4*5/4

.....

1 - 1/100^2 = (1 - 1/100)(1 + 1/100) = 99/100*101/100

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P = 1/2*3/2*2/3*4/3*3/4*5/4*...*99/100*101/100

= 1/2*101/100 = 101/200