Question

1/2+2/4+3/8+4/16+.+10/1024

Answer 1

设结果为s,则s=1/2+2/2^2+3/2^3+4/2^4+……+10/2^10,那么(1/2)s=1/2^2+2/2^3+3/2^4+4/2^5+……+10/2^11.求s-(1/2)s=1/2+1/2^2+1/2^3+……+1/2^2^10-10/2^11=（1/2(1-1/2^10)）/（1-1/2）-10/2^11=1-1/2^10-10/2^11=509/512.结果1/2s=509/512,那么s=1018/512.