1+2+2的2次方+2的3次方+2的4次方……+2的1000次方=

2^0+2^1+2^2+2^3+2^4+2^5……2^1000 =1+2^0+2^1+2^2+2^3+2^4+2^5……2^1000-1 =2^0+2^0+2^1+2^2+2^3+2^4+2^5……2^1000-1 =2^1+2^1+2^2+2^3+2^4+2^5……2^1000-1 =2^2+2^2+2^3+2^4+2^5……2^1000-1 …… =2^1001-1