数学简便计算题(平方差公式)
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数学简便计算题(平方差公式)
一、(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/99²)(1-1/100²)
二、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
一、(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/99²)(1-1/100²)
二、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
![数学简便计算题(平方差公式)](/uploads/image/z/939222-54-2.jpg?t=%E6%95%B0%E5%AD%A6%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%E9%A2%98%EF%BC%88%E5%B9%B3%E6%96%B9%E5%B7%AE%E5%85%AC%E5%BC%8F%EF%BC%89)
一、(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).(1-1/100)(1+1/100)
=1/2x3/2x2/3x...x99/100x101/100
=1/2x101/100
=101/200
二、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
=2*(1-1/2)、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
=2*(1-1/2²)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
=.
=2*(1-1/2^16)+1/2^15
=2-1/2^15+1/2^15
=2
如追加其它问题,采纳本题后点击想我求助,
=(1-1/2)(1+1/2)(1-1/3)(1+1/3).(1-1/100)(1+1/100)
=1/2x3/2x2/3x...x99/100x101/100
=1/2x101/100
=101/200
二、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
=2*(1-1/2)、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
=2*(1-1/2²)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
=.
=2*(1-1/2^16)+1/2^15
=2-1/2^15+1/2^15
=2
如追加其它问题,采纳本题后点击想我求助,