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1/(k(k+1))=1/k - 1/(k+1)

1kk11k 1k1 class=

Răspuns :

Răspuns:

Explicație pas cu pas:

prima paranteza de sub radical:

1/1-1/2+1/2-1/3+1/3-1/4+.........1/36-1/37=1-1/37=36/37

a doua paranteza:

1/37-1/38+1/38-1/39+1/39-1/40+......1/73-1/74=1/37-1/74

scaderea parantezelor:

36/37 - 1/37+1/74=35/37 + 1/74=(70+1)/74

inmultirea finala:

(74/71)ꞏ(71/74)=1

raspuns final x=1