第2、3题！要过程！简便！谢谢！会加分！
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2. = (1/2)*(3/2)*(2/3)*(4/3)*(3/4)*(4/5)* …… *(99/100)*(101/100)
=(1/2) * (101/100)
= 101/200
3. = 1 * (2+1)*(2^2 + 1) * (2^4 + 1) * (2^8 + 1) * (2^16 + 1) * (2^32 + 1) * (2^64 + 1)
= (2-1)*(2+1) * (2^2 + 1) * (2^4 + 1) * (2^8 + 1) * (2^16 + 1) * (2^32 + 1) * (2^64 + 1)
= (2^2 - 1) * (2^2 + 1) * (2^4 + 1) * (2^8 + 1) * (2^16 + 1) * (2^32 + 1) * (2^64 + 1)
…………
= 2^128 - 1
=(1/2) * (101/100)
= 101/200
3. = 1 * (2+1)*(2^2 + 1) * (2^4 + 1) * (2^8 + 1) * (2^16 + 1) * (2^32 + 1) * (2^64 + 1)
= (2-1)*(2+1) * (2^2 + 1) * (2^4 + 1) * (2^8 + 1) * (2^16 + 1) * (2^32 + 1) * (2^64 + 1)
= (2^2 - 1) * (2^2 + 1) * (2^4 + 1) * (2^8 + 1) * (2^16 + 1) * (2^32 + 1) * (2^64 + 1)
…………
= 2^128 - 1
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两题都要利用平方差公式。
2、原式
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)…(1-1/100)(1+1/100)
=1/2x3/2x2/3x4/3…x99/100x101/100
=1/2x101/100
=101/200
3、原式
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/(2-1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=2^128-1
2、原式
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)…(1-1/100)(1+1/100)
=1/2x3/2x2/3x4/3…x99/100x101/100
=1/2x101/100
=101/200
3、原式
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/(2-1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=2^128-1
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