Răspuns:
Explicație pas cu pas:
1/(1·2) + 1/(2·3) + 1/(3·4) +......+1/[n·(n+1)] = n/(n+1) ; n ∈N*
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1/(1·2) + 1/(2·3) + 1/(3·4) +......+1/[n·(n+1)] = x
x = 1/2 + 1/6 + 1/12 +.....+1/[n·(n+1)] <=>
x = (1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) +........+ [1/n - 1/(n+1)]
Se reduc termenii -1/2+1/2 ......=>
x = 1 - 1/(n+1) = (n+1-1)/(n+1) =>
x = n/(n+1) ; n ∈N*
