数学题(1+1/2)(1+1/22)(1+1/24)(1+1/28)+1/215(1+1/2)(1+1/22)(1+1/24)(1+1/28)+1/215怎么计算 用乘法公式简化计算
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![数学题(1+1/2)(1+1/22)(1+1/24)(1+1/28)+1/215(1+1/2)(1+1/22)(1+1/24)(1+1/28)+1/215怎么计算 用乘法公式简化计算](/uploads/image/z/247909-13-9.jpg?t=%E6%95%B0%E5%AD%A6%E9%A2%98%EF%BC%881%2B1%2F2%EF%BC%89%EF%BC%881%2B1%2F22%EF%BC%89%EF%BC%881%2B1%2F24%EF%BC%89%EF%BC%881%2B1%2F28%EF%BC%89%2B1%2F215%EF%BC%881%2B1%2F2%EF%BC%89%EF%BC%881%2B1%2F22%EF%BC%89%EF%BC%881%2B1%2F24%EF%BC%89%EF%BC%881%2B1%2F28%EF%BC%89%2B1%2F215%E6%80%8E%E4%B9%88%E8%AE%A1%E7%AE%97+%E7%94%A8%E4%B9%98%E6%B3%95%E5%85%AC%E5%BC%8F%E7%AE%80%E5%8C%96%E8%AE%A1%E7%AE%97)
数学题(1+1/2)(1+1/22)(1+1/24)(1+1/28)+1/215(1+1/2)(1+1/22)(1+1/24)(1+1/28)+1/215怎么计算 用乘法公式简化计算
数学题(1+1/2)(1+1/22)(1+1/24)(1+1/28)+1/215
(1+1/2)(1+1/22)(1+1/24)(1+1/28)+1/215
怎么计算 用乘法公式简化计算
数学题(1+1/2)(1+1/22)(1+1/24)(1+1/28)+1/215(1+1/2)(1+1/22)(1+1/24)(1+1/28)+1/215怎么计算 用乘法公式简化计算
(1+1/2)(1+1/22)(1+1/24)(1+1/28)+1/215
乘以1-1/2,再除以1-1/2
=(1-1/2)(1+1/2)(1+1/22)(1+1/24)(1+1/28)/(1-1/2)+1/215
平方差
=(1-1/22)(1+1/22)(1+1/24)(1+1/28)/(1/2)+1/215
=(1-1/24)(1+1/24)(1+1/28)/(1/2)+1/215
=(1-1/28)(1+1/28)/(1/2)+1/215
=2×(1-1/216)+1/215
=2×1-2×1/216+1/215
=2-1/215+1/215
=2
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15
=2*(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15
=2*(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15
=2*(1-1/2^4)(1+1/2^4)(1+1/2^8)+1/2^15
=2*(1-1/2^8)(1+1/2^8)+1/2^15
=2*(1-1/2^16)+1/2^15
=2-1/2^15+1/2^15
=2
(1+1/2)(1+1/22)(1+1/24)(1+1/28)+1/215
=(1-1/2)(1+1/2)(1+1/22)(1+1/24)(1+1/28)*2+1/215
一直用平方差公式,有:
原式=(1-1/2^16)*2+1/2^15
=2-1/2^15+1/2^15
=2
(1+1/2)(1+1/22)(1+1/24)(1+1/28)+1/215
(乘以1-1/2,再除以1-1/2)
=(1-1/2)(1+1/2)(1+1/22)(1+1/24)(1+1/28)/(1-1/2)+1/215
=(1-1/22)(1+1/22)(1+1/24)(1+1/28)/(1/2)+1/215
=(1-1/24)(1+1/24)(1+1/28)/(...
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(1+1/2)(1+1/22)(1+1/24)(1+1/28)+1/215
(乘以1-1/2,再除以1-1/2)
=(1-1/2)(1+1/2)(1+1/22)(1+1/24)(1+1/28)/(1-1/2)+1/215
=(1-1/22)(1+1/22)(1+1/24)(1+1/28)/(1/2)+1/215
=(1-1/24)(1+1/24)(1+1/28)/(1/2)+1/215
=(1-1/28)(1+1/28)/(1/2)+1/215=2×1-2×1/216+1/215
=2-1/215+1/215
=2
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