Question

超简单的小学数学问题（简算题）

1/2+3/4+7/8+15/16+31/32+63/64+127/128=？
简算

Answer 1

1/2+3/4+7/8+15/16+31/32+63/64+127/128
=1/2+(1-1/4)+(1-1/8)+(1-1/16)+(1-1/32)+(1-1/64)+(1-1/128)
=1/2+6-(1/4+1/8+1/16+1/32+1/64+1/128)
=7-(1/2+1/2^2+1/2^3+1/2^4+1/2^5+1/2^6+1/2^7)
=7-(1-1/2^7)·············注：直接用等比数列求和公式；
=6+1/2^7
=6+1/128
=769/128

也可以
设A=1/2+1/2^2+1/2^3+1/2^4+1/2^5+1/2^6+1/2^7
在A的两边同乘以1/2，得
1/2A=1/2^2+1/2^3+...+1/2^7+1/2^8
两式相减，得
A-1/2A=1/2-1/2^8
1/2A=1/2-1/2^8
A=1-1/2^7

Answer 2

6.007812

Answer 3

64/128+96/128+120/128+124/128+126/128+127/128
=(64+96+120+124+126+127)/128
=657/128

Answer 4

1/2+3/4+7/8+15/16+31/32+63/64+127/128=？
=64/128+96/128+112/128+120/128+124/128+126/128+127/128
=(64+96+112+120+124+126+127)/128
=769/128

Answer 5

什么

Answer 6

不就是54/128+96/128+112/128+120/128+124/128+127/128
＝769／128