Question

2的99次方+2的98次方+2的97次方+···+2+1等于多少

Answer 1

令S=2^99+2^98+2^97+.+2+1

2S=2^100+2^99+2^98+2^97+.+2^2+2

2S-S=2^100-1

S=2^100-1

即2^99+2^98+2^97+.+2+1=2^100-1