问几道数学题,要把我教会,(1).100^2-99^2+98^2-97^2+.+2^2-1^2=_?(2).(1-1/2^2)(1-1/3^2)(1-1/4^2)...(1-1/10^2)=_?(3).(2+1)(2^2+1)(2^4+1).(2^32+1)=_?
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问几道数学题,要把我教会,(1).100^2-99^2+98^2-97^2+.+2^2-1^2=_?(2).(1-1/2^2)(1-1/3^2)(1-1/4^2)...(1-1/10^2)=_?(3).(2+1)(2^2+1)(2^4+1).(2^32+1)=_?
问几道数学题,要把我教会,
(1).100^2-99^2+98^2-97^2+.+2^2-1^2=_?
(2).(1-1/2^2)(1-1/3^2)(1-1/4^2)...(1-1/10^2)=_?
(3).(2+1)(2^2+1)(2^4+1).(2^32+1)=_?
问几道数学题,要把我教会,(1).100^2-99^2+98^2-97^2+.+2^2-1^2=_?(2).(1-1/2^2)(1-1/3^2)(1-1/4^2)...(1-1/10^2)=_?(3).(2+1)(2^2+1)(2^4+1).(2^32+1)=_?
(1).100^2-99^2+98^2-97^2+96^2-95^2……+2^2-1^2
=(100-99)(100+99)+(98-97)(98+97)+……+(2-1)(2+1)
=100+99+98+……+1
=5050
(2).(1-1/2^2)(1-1/3^2)(1-1/4^2)...(1-1/10^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3).(1-1/10)(1+1/10)
=(1-1/2)(1-1/3)...(1-1/10)*(1+1/2)(1+1/3)...(1+1/10)
=(1/2)(2/3)...(9/10)*(3/2)(4/3)...(11/10)
=(1/10)(11/2)
=11/20
(3).(2+1)(2^2+1)(2^4+1).(2^32+1)
=(2-1)*(2+1)*(2^2+1)*(2^4+1)……(2^32+1)
=[(2-1)*(2+1)]*(2^2+1)*(2^4+1)……(2^32+1)
=(2^-1)*(2^2+1)*(2^4+1)……(2^32+1)
=(2^4-1)*(2^4+1)……(2^32+1)
=(2^8-1)*(2^8+1)……(2^32+1)
=.
=(2^32-1)*(2^32+1)
=2^64-1