数学简算题(1+1/5)(1+1/5^2)(1+1/5^4)...(1+1/5^32),
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数学简算题(1+1/5)(1+1/5^2)(1+1/5^4)...(1+1/5^32),
![数学简算题(1+1/5)(1+1/5^2)(1+1/5^4)...(1+1/5^32),](/uploads/image/z/5363730-18-0.jpg?t=%E6%95%B0%E5%AD%A6%E7%AE%80%E7%AE%97%E9%A2%98%281%2B1%2F5%29%281%2B1%2F5%5E2%29%281%2B1%2F5%5E4%29...%281%2B1%2F5%5E32%29%2C)
(1+1/5)(1+1/5^2)(1+1/5^4)...(1+1/5^32)
=(1-1/5)(1+1/5)(1+1/5^2)(1+1/5^4)(1+1/5^8)……(1+1/5^32)/(1-1/5)
=(1-1/5^2)(1+1/5^2)(1+1/5^4)(1+1/5^8)……(1+1/5^32)/(1-1/5)
=……
=(1-1/5^64)/(1-1/5)
=4(1-1/5^64)/5
=(1-1/5)(1+1/5)(1+1/5^2)(1+1/5^4)(1+1/5^8)……(1+1/5^32)/(1-1/5)
=(1-1/5^2)(1+1/5^2)(1+1/5^4)(1+1/5^8)……(1+1/5^32)/(1-1/5)
=……
=(1-1/5^64)/(1-1/5)
=4(1-1/5^64)/5
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