(2+1)(4+1)(16+1)(256+1)=?怎样算

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(2+1)(4+1)(16+1)(256+1)=?怎样算

(2+1)(4+1)(16+1)(256+1)=?怎样算
(2+1)(4+1)(16+1)(256+1)=?怎样算

(2+1)(4+1)(16+1)(256+1)=?怎样算
3*5*17*257=65535

不会

(2+1)(2^2+1)(2^4+1)(2^8+1)
=

(2+1)(4+1)(16+1)(256+1)=(1+1+1+1)+(16+4)+(256+2)=282

(2+1)(4+1)(16+1)(256+1)
=(2+1)(2^2+1)(2^4+1)(2^8+1) (把每项乘开)
=2^15+2^14+2^13+......+2^3+2^2+2^1+2^0(等比数列)
=(1-2^16)/(1-2)
=65535

(2+1)(4+1)(16+1)(256+1)
=(2-1)(2+1)(4+1)(16+1)(256+1)
=(4-1)(4+1)(16+1)(256+1)
=(16-1)(16+1)(256+1)
=(256-1)(256+1)
=65536-1
=65535
这题要用平方差的~公式是:(a+b)(a-b)=a平方-b平方

如果问题是 3*5*17*257，还会有人想到楼上的答案吗

原式等于
(4-1)(4+1)(16+1)(256+1)
=(16-1))(16+1)(256+1)
=(256-1)(256+1)
=65535

(2+1)(4+1)(16+1)(256+1)怎么算? 1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 1/2-1/4-1/8-16/1-32/1-64/1-128/1-256/1 （1+1/2)(1+1/4）（1+1/16)(1+1/256) 等于多少?快 1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256 （1+1/2)(1+1/4）（1+1/16)(1+1/256) 等于多少? 1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 初一(1+1/2)(1+1/4)(1+1/16)(1+1/256)(1-1/2)*(1+1/2)*(1+1/4)*(1+1/16))*(1+1/256)/(1-1/2)=(1-1/256*1/256)/(1-1/2)=2-2/256*256 (x-1/2)(2x+1)(2x^2+1/2)(4x^4+1/4)(16x^6+1/16)/(256x^16-1/256) (x-1/2)(2x+1)(2x^2+1/2)(4x^4+1/4)(16x^8+1/16)÷(256x^16+1/256)=? (x-1/2)(2x+1)(2x^2+1/2)(4x^4+1/4)(16x^6+1/16)/(256x^16+1/256)=? 计算：1/2+1/4+1/8+1/16+1/64+1/128+1/256 1-1/2-1/4-1/8-1/16-1/32-.1/256 利用平方差公式计算：（1+1/2)×（1+1/4)×(1+1/16)×（1/256) 1+1/2+1/4+1/8+1/16+1/32.+1/256 ? 简便计算1/2+1/4+1/8+1/16+.+1/128+1/256 1/2+1/4+1/8+1/16+1/32+...+1/256简便运算 1/2+1/4+1/8+1/16+1/32+...+1/256简便运算