作业帮8128 所有因数倒数之和是多少?
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8128 所有因数倒数之和是多少?
8128 所有因数倒数之和是多少?
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