Question

S=2la puterea 0 +2la puterea 1+2la puterea 2 +2la puterea 3 +......+2 la puterea 99

Answer 1

 1)   S= 2^0+2^1+...+2^99  /inmultim cu 2 (in ambele parti) si avem:
2)2*S=         2^1+...+2^99+2^100
 -------------------------------------------- scadem 2) -1) si avem
2*S-S=2^1...+2^99+2^100-(2^0+2^1...+2^99) =>
=> S= 2^100-2^0, adica S=2^100 -1