Răspuns:
Explicație pas cu pas:
1/1x2 + 1/2x3 + 1/3×4 + ... + 1/31×32
1/1x2 = 1 - 1/2
1/2x3 = 1/2 - 1/3
1/3x4 = 1/3 - 1/4
.....................
1/31x32 = 1/31 - 1/32
_____________________
1/1x2 + 1/2x3 + 1/3×4 + ... + 1/31×32 = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/31 - 1/32
1/1x2 + 1/2x3 + 1/3×4 + ... + 1/31×32 = 1 - 1/32 = 32/32 - 1/32 = 31/32