1.1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/2562.(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*……*(1+1/99)*(1-1/99)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/28 21:12:44
1.1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/2562.(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*……*(1+1/99)*(1-1/99

1.1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/2562.(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*……*(1+1/99)*(1-1/99)
1.1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256
2.(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*……*(1+1/99)*(1-1/99)

1.1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/2562.(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*……*(1+1/99)*(1-1/99)
1.
=1-1/2+1-1/4+1-1/8+...+1-1/256
=8-(1/2+1/4+1/8+...+1/256) 根据等比数列求和公式
=8-(1-1/256)
=7又1/256
2.
=3/2 * 1/2 * 4/3 * 2/3 * 5/4 * 3/4 * 6/5 * 4/5 *...*100/99 * 98/99
相隔其他两项的两项都消去了,如3/2和2/3,4/3和3/4
=1/2*100/99
=50/99

1.原式=(1-1/2)+(1-1/4)+(1-1/8)+(1-1/16)+(1-1/32)+(1-1/64)+(1-1/128)+(1-1/256)
=8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256)
=8-(128+64+32+16+8+4+2+1)/256
=8-255/256
=7又1/256