1/2+1/4+1/8+1/16+1/32.+1/1024                   

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1/2+1/4+1/8+1/16+1/32.+1/1024                   

1/2+1/4+1/8+1/16+1/32.+1/1024                   
1/2+1/4+1/8+1/16+1/32.+1/1024                 
 
 

1/2+1/4+1/8+1/16+1/32.+1/1024                   
1/2+1/4+1/8+1/16+1/32+1/64+.+1/1024
=1/2+1/4+1/8+1/16+1/32+1/64+.+1/1024 +1/1024-1/1024
=1/2+1/4+1/8+1/16+1/32+1/64+.+1/512-1/1024
.
=1-1/1024
=1023/1024

1/2+1/4+1/8+1/16+1/32+1/64+.....+1/1024
=1/2+1/4+1/8+1/16+1/32+1/64+.....+1/1024 +1/1024-1/1024
=1/2+1/4+1/8+1/16+1/32+1/64+.....+1/512-1/1024
........
=1-1/1024
=1023/1024


设原式= A
则:
A= -1/2+1/4-1/8+1/16-1/32+1/64-......+1/1024
2A= -1+1/2-1/4+1/8-1/16+1/32-1/64+......+1/512
两式相加,中间各项正负相消,得:
3A= -1+1/1024= -1023/1024
所以:
A= -341/1024
即...

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设原式= A
则:
A= -1/2+1/4-1/8+1/16-1/32+1/64-......+1/1024
2A= -1+1/2-1/4+1/8-1/16+1/32-1/64+......+1/512
两式相加,中间各项正负相消,得:
3A= -1+1/1024= -1023/1024
所以:
A= -341/1024
即:
-1/2+1/4-1/8+1/16-1/32+1/64-......+1/1024= -341/1024
这个是以1/2为公比的等比数列
1/2+1/4+1/8+1/16+1/32+1/64+.....+1/1024
=1/2+1/4+1/8+1/16+1/32+1/64+.....+1/2^10
=(1/2)(1-(1/2)^10)/(1/2)=1023/1024

收起

1023/1024

等比数列的求和公式。
1/2+1/2的平方+........1/2的十次方
公式为[1/2(1-1/2的十次方)]/1-1/2
答案是1-1/2的十次方
就是1023/1024

令a=1/2+1/4+1/8+1/16+1/32...........+1/1024
两边乘2
2a=2*(1/2+1/4+1/8+1/16+1/32...........+1/1024)
=1+1/2+1/4+1/8+1/16+1/32...........+1/512
相减
a=2a-a=1-1/1024=1023/1024
所以1/2+1/4+1/8+1/16+1/32...........+1/1024
=1023/1024

1/2+1/4+1/8+1/16+1/32+1/64+.....+1/1024
=1/2+1/4+1/8+1/16+1/32+1/64+.....+1/1024 +1/1024-1/1024
=1/2+1/4+1/8+1/16+1/32+1/64+.....+1/512-1/1024
........
=1-1/1024
=1023/1024
设...

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1/2+1/4+1/8+1/16+1/32+1/64+.....+1/1024
=1/2+1/4+1/8+1/16+1/32+1/64+.....+1/1024 +1/1024-1/1024
=1/2+1/4+1/8+1/16+1/32+1/64+.....+1/512-1/1024
........
=1-1/1024
=1023/1024
设原式= A
则:
A= -1/2+1/4-1/8+1/16-1/32+1/64-......+1/1024
2A= -1+1/2-1/4+1/8-1/16+1/32-1/64+......+1/512
两式相加,中间各项正负相消,得:
3A= -1+1/1024= -1023/1024
所以:
A= -341/1024
即:
-1/2+1/4-1/8+1/16-1/32+1/64-......+1/1024= -341/1024

收起

=(1-1/2)+(1/2-1/4)+(1/4-1/8)+.....+(1/512-1/1024)
=1-1/1024
=1023/1024
Ha!Ha!OK!了!
一定要选我。。

=1-1/2+1/2-1/4+1/4-1/8+......+1/256-1/512+1/512-1/1024
=1-1/1024
=1023/1024

1-1/2+1/2-1/4......+1/512-1/1024=1-1/1024=1023/1024

比值为1/2的等比数列,即1/2^1+1/2^2+……+1/2^10,n=10
Sn=a1(1-q^n)/(1-q) ={1/2*[1-(1/2)^10]}/(1-1/2)=1023/1024
或1/2+1/4=3/4,1/2+1/4+1/8=7/8,1/2+1/4+1/8+1/16=15/16,……
1/2+1/4+1/8+1/16+1/32...........+1/1024=1023/1024

原式=(1/2)^1+(1/2)^2+(1/2)^3+......(1/2)^10
a=1/2 q=1/2
由s=a(1—q^10)/(1-q) 得,
原式=1023/1024

1/2+1/4+1/8+1/16+1/32+1/64+.....+1/1024
=1/2+1/4+1/8+1/16+1/32+1/64+.....+1/2^10
=(1/2)(1-(1/2)^10)/(1/2)=1023/1024