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数学题(1+1/2)

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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