(复杂)有理数指数幂计算
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(复杂)有理数指数幂计算
有理数指数幂计算:(1+2^1\32)(1+2^1\16)(1+2^1\8)(1+2^1\4)(1+2^1\2):(1+2^1\32)(1+2^1\16)(1+2^1\8)(1+2^1\4)(1+2^1\2)
有理数指数幂计算:(1+2^1\32)(1+2^1\16)(1+2^1\8)(1+2^1\4)(1+2^1\2):(1+2^1\32)(1+2^1\16)(1+2^1\8)(1+2^1\4)(1+2^1\2)
![(复杂)有理数指数幂计算](/uploads/image/z/8588809-1-9.jpg?t=%EF%BC%88%E5%A4%8D%E6%9D%82%EF%BC%89%E6%9C%89%E7%90%86%E6%95%B0%E6%8C%87%E6%95%B0%E5%B9%82%E8%AE%A1%E7%AE%97)
(1+2^1/32)(1+2^1/16)(1+2^1/8)(1+2^1/4)(1+2^1/2)
上下同乘以(1-2^1/32),反复用平方差
=(1-2^1/32)(1+2^1/32)(1+2^1/16)(1+2^1/8)(1+2^1/4)(1+2^1/2)/(1-2^1/32)
=[1^2-(2^1/32)^2](1+2^1/32)(1+2^1/16)(1+2^1/8)(1+2^1/4)(1+2^1/2)/(1-2^1/32)
=(1-2^1/16)(1+2^1/16)(1+2^1/8)(1+2^1/4)(1+2^1/2)/(1-2^1/32)
=(1-2^1/8)(1+2^1/8)(1+2^1/4)(1+2^1/2)/(1-2^1/32)
=(1-2^1/4)(1+2^1/4)(1+2^1/2)/(1-2^1/32)
=(1-2^1/2)(1+2^1/2)/(1-2^1/32)
=(1-2)/(1-2^1/32)
=-1/(1-2^1/32)
=1/(2^1/32-1)
上下同乘以(1-2^1/32),反复用平方差
=(1-2^1/32)(1+2^1/32)(1+2^1/16)(1+2^1/8)(1+2^1/4)(1+2^1/2)/(1-2^1/32)
=[1^2-(2^1/32)^2](1+2^1/32)(1+2^1/16)(1+2^1/8)(1+2^1/4)(1+2^1/2)/(1-2^1/32)
=(1-2^1/16)(1+2^1/16)(1+2^1/8)(1+2^1/4)(1+2^1/2)/(1-2^1/32)
=(1-2^1/8)(1+2^1/8)(1+2^1/4)(1+2^1/2)/(1-2^1/32)
=(1-2^1/4)(1+2^1/4)(1+2^1/2)/(1-2^1/32)
=(1-2^1/2)(1+2^1/2)/(1-2^1/32)
=(1-2)/(1-2^1/32)
=-1/(1-2^1/32)
=1/(2^1/32-1)