Question

1+2/2+3/4 +4/8+5/16+.........

Answer 1

S = 1/2 + 1/4 + 2/8 + 3/16 + 5/32 + 8/64 + 13/128 + ...

then

S/2 = 1/4 + 1/8 + 2/16 + 3/32 + 5/64 + 8/128 + ...

then get 2S from the first line:

2S = 1 + 1/2 + 2/4 + 3/8 + 5/16 + 8/32 + 13/64 + ...

This is the big line:

2S - S/2 = S + 1

Therefore S = 2

HOPE THIS HELPS