Найти значение оптимальным способом 1/2*3+1/3*4+1/4*5+.......1/19*20=?
(сумма дробей, знак / - деление, * - умножение)
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Verified answer
1/(2*3) = 1/2 -1/31/(3*4) = 1/3 - 1/4
1/(4*5) = 1/4 - 1/5
.......
1/(19*20) = 1/19 - 1/20
1/(2*3)+1/(3*4)+1/(4*5)+.......1/(19*20) = 1/2 -1/3 + 1/3 - 1/4 +1/4 - 1/5+ ...+ 1/19 - 1/20 = 1/2 -1/20 = 9/20 = 0,45