用简便方法计算下列各式

(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/99²)(1-1/100²)

=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)……(1+1/99)(1-1/99)(1+1/100)(1-1/100)
=(3/2x4/3x5/4x……x100/99x101/100)x(1/2x2/3x3/4x……x98/99x99/100)
=101/2x1/100
=101/200

(1+1/2)(1+1/2²)(1+1/2^4)(1+1/2^8)+1/2^15

=(1-1/2)(1+1/2)(1+1/2²)(1+1/2^4)(1+1/2^8)/(1-1/2)+1/2^15
=(1-1/2²)(1+1/2²)(1+1/2^4)(1+1/2^8)x2+1/2^15
=(1-1/2^4)(1+1/2^4)(1+1/2^8)x2+1/2^15
=(1-1/2^8)(1+1/2^8)x2+1/2^15
=(1-1/2^16)x2+1/2^15
=2-1/2^15+1/2^15
=2

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