1)50^2-49^2+48^2-47^2.+2^2-1^2
=(50-49)(50+49)+(48-47)(48+47).+(2-1)(2+1)
=1(50+49)+1(48+47)+.1(2+1)
=50+49+48+47+.2+1
=(50+1)*50/2
2)=(10+1)(100+1)(10000+1)
=(10+1)(100+1)(100^2+1)
=分子:(10+1)(100+1)(100^2+1)*((10-1)(100-1)(100^2-1))/分母:((10-1)(100-1)(100^2-1))
=分子:(10+1)(10-1)(100+1)(100-1)(100^2+1)(100^2-1)/分母(10-1)(100-1)(100^2-1)
=分子:(100-1)(100^2-1)(10000^2-1)/分母(10-1)(100-1)(100^2-1)
上下约分
=分子(10000^2-1)/分母(10-1)
=(100000000-1)/(10-1)
=99999999/9
=11111111
3)=(1-1/2)(1+1/2)(1-1/3)(1+1/3).(1-1/9)(1+1/9)(1-1/10)(1+1/10)
=1/2*3/2*2/3*4/3*3/4*5/4.*8/9*10/9*9/10*11/10
类似于3/2*2/3的都可以约掉
=1/2*11/10
=11/20
4)首先,2^5=32,2^6=64,
(2^96-1)
=(2^48-1)(2^48+1)
=(2^24-1)(2^24+)(2^48+1)
=(2^12-1)(2^12+1)(2^24+)(2^48+1)
=(2^6-1)(2^6+1)(2^12+1)(2^24+)(2^48+1)
=63*65*(2^12+1)(2^24+)(2^48+1)
所以是63,65