一道计算题,求高手帮忙!1/2+1/4+1/8+1/16+1/128+1/256+…+1/2^n计算:1/2+1/4+1/8+1/16+1/128+1/256+…+1/2^n急!

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一道计算题,求高手帮忙!1/2+1/4+1/8+1/16+1/128+1/256+…+1/2^n计算:1/2+1/4+1/8+1/16+1/128+1/256+…+1/2^n急!一道计算题,求高手帮忙

一道计算题,求高手帮忙!1/2+1/4+1/8+1/16+1/128+1/256+…+1/2^n计算:1/2+1/4+1/8+1/16+1/128+1/256+…+1/2^n急!
一道计算题,求高手帮忙!1/2+1/4+1/8+1/16+1/128+1/256+…+1/2^n
计算:1/2+1/4+1/8+1/16+1/128+1/256+…+1/2^n
急!

一道计算题,求高手帮忙!1/2+1/4+1/8+1/16+1/128+1/256+…+1/2^n计算:1/2+1/4+1/8+1/16+1/128+1/256+…+1/2^n急!
x=1/2+1/4+1/8+1/16+1/128+1/256+…+1/2^n
2x=1+1/2+1/4+1/8+1/16+1/128+1/256+…+1/2^n-1
两式相减,x=1-1/2^n

以1/2+1/4+1/8为例,等于7/8,可看出分子比分母少1
则该题同理,原式=2的n次幂分之2的n次幂-1

1/2+1/4+1/8+1/16+1/128+1/256+…+1/2^n
=1-1/2^n