formula pentru numere consecutive :
1 / n · ( n +1 ) = 1 / n - 1 / ( n +1)
cu formula ⇒ fiecare termen devine o scadere
1 / 1 · 2 = 1 / 1 - 1 /2
1 / 2 · 3 = 1 /2 - 1 /3
1 / 3 · 4 = 1 /3 - 1 /4
..................................
1 /n·( n +1) = 1 / n - 1 / ( n +1 )
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suma din ex . = 1 / 1 - 1 / ( n +1) [ ceilalti , cate doi calculati =0 ]
( n + 1 - 1 ) / ( n +1 ) = n / ( n +1) = 100 /101 = 100 / ( 100 + 1)
⇒ n =100
