简算:(2+1)(2^2+1)(2^4+1)…(2^32+1)+1
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简算:(2+1)(2^2+1)(2^4+1)…(2^32+1)+1简算:(2+1)(2^2+1)(2^4+1)…(2^32+1)+1简算:(2+1)(2^2+1)(2^4+1)…(2^32+1)+1你
简算:(2+1)(2^2+1)(2^4+1)…(2^32+1)+1
简算:(2+1)(2^2+1)(2^4+1)…(2^32+1)+1
简算:(2+1)(2^2+1)(2^4+1)…(2^32+1)+1
你可以先找找规律
2+1=2^1+2^0
(2+1)(2^2+1)=2^3+2^2+2^1+2^0
(2+1)(2^2+1)(2^4+1)=(2^3+2^2+2^1+2^0)(2^4+1)=2^7+……+2^0
所以归纳得到(2+1)(2^2+1)(2^4+1)…(2^32+1)=2^63+……+2^0
所以原式=2^63+……+2^0+1=(1-2^64)/(1-2)+1=2^64
(2+1)(2^2+1)(2^4+1)…(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1)…(2^32+1)+1
=(2^4-1)(2^4+1)…(2^32+1)+1
=......
=(2^32-1)(2^32+1)+1
=2^64