【数学】计算1-1/2-1/4-1/8-…-1/64-1/128-1/256.

显示全部楼层 · 2013-10-9 18:15:20

解：原式=1-（1-1/2)-(1/2-1/4)-(1/4-1/8)-……-(1/32-1/64)-(1/64-1/128)-(1/128-1/256)
=1-1+1/2-1/2+1/4-1/4+1/8-……-1/32+1/64-1/64+1/128-1/128+1/256
=1/256施主，我看你骨骼清奇，器宇轩昂,且有慧根,乃是万中无一的武林奇才.潜心修习,将来必成大器，鄙人有个小小的考验请点击在下答案旁的 "选为满意答案"...

千问 · 2013-10-9 18:15:20

1-1/2-1/4-1/8-…-1/64-1/128-1/256.=(1-1/2)-1/4-1/8-........1/64-1/128-1/256=1/2-1/4-1/8-…-1/64-1/128-1/256=1/4-1/8-…-1/64-1/128-1/256=.......=1/128-1/256=1/256...

千问 · 2013-10-9 18:15:20

1-1/2-1/4-1/8-…-1/64-1/128-1/256=1-1/2-1/4-1/8-…-1/64-1/128-1/256-1/256+1/256=1-1/2-1/4-1/8-…-1/64-1/128-（1/256+1/256）+1/256=1-1/2-1/4-1/8-…-1/64-1/128-（1/128）+1/256=1-1/2-...

千问 · 2013-10-9 18:15:20

=1-（1-1/2)-(1/2-1/4)-(1/4-1/8)-……-(1/32-1/64)-(1/64-1/128)-(1/128-1/256)
=1-1+1/2-1/2+1/4-1/4+1/8-……-1/32+1/64-1/64+1/128-1/128+1/256 =1/256...