Question

1+2la puterea0+2la puterea1+2la puterea2+......+2la puterea9=

Answer 1

S=1+2^0+2^1+2^2+.......+2^9
Inmultind cu 2 obtinem:
2·S=1*2+2^0*2+2^1*2+2^2*2+....+2^9*2
2·S=2+2^(0+1)+2^(1+1)+2^(2+1)+.....+2^(9+1)
2·S=2+2^1+2^2+2^3+.....+2^10
2·S=(1+2^0+2^1+2^2+....+2^9)+2^10-2^0+1
Asadar:
2·S=S+2^10-2^0+1
De unde:
S=2^10-2^0+1
S=2^10-1+1
S=2^10
S=1024