1 /( k + 1 ) - 1 / ( k +3) = 1 /2 · [ 1 /( k+1 ) - 1 / ( k +3 ) ]
k =0 ,,,,, = 1 /2 [ 1 /1 - 1 /3 ]
k =1 = 1 /2 [ 1 /2 - 1 /4 ]
k=2 = 1 /2 [ 1 /3 - 1 /5 ]
.................................................................
k = n -1 = 1 /2 [ 1 / n - 1 / ( n +2) ]
k=n = 1 /2 [ 1 /( n +1 ) - 1 / ( n +3) ]
suma = 1 /2 · [ 1 + 1 /2 - 1 / ( n+2) -1 /(n +3) ]
= 1 /2 · [ 3/2 - ( 2n +5) / ( n +2 ) · ( n +3) ]
sirul = 4/3 · 3/4 - 4/3 · 1/2 · ( 2n+5) / ( n+2) · ( n+ 3) ]
= 1 - 2/3 ·(2n+5) / ( n +2) ·( n +3 ) construim definitia e
- 4 /3 - 4
lim = e = ∛ e
