学帮网8128 所有因数倒数之和是多少?
来源：学生作业学帮网 编辑：学帮网 时间：2024/05/12 20:33:20
8128 所有因数倒数之和是多少?
8128所有因数有：
1,2,4,8,16,32,64,127,2*127,4*127,8*127,16*127,32*127,64*127
倒数之和是
1+1/2+1/4+1/8+1/16++1/32+1/64+1/127(1+1/2+1/4+1/8+1/161+1/32+1/64)
=(1+1/2+1/4+1/8+1/16+1/32+1/64)(1+1/127)
=((64+32+16+8+4+2+1)/64)(128/127)
=(127/64)(128/127)
=2
8128=2的6次方*127,其因数共有14个,为
1,2,4,8,16,32,64,127,2*127,4*127,8*127,16*127,32*127,64*127
倒数之和是
1+1/2+1/4+1/8+1/16++1/32+1/64+1/127(1+1/2+1/4+1/8+1/161+1/32+1/64)
=(1+1/2+1/4+1/8+1/16+1/32+1/64)(1+1/127)
=((64+32+16+8+4+2+1)/64)(128/127)
=(127/64)(128/127)
=2