(1²+3²+…+99²)÷(2²+4²+…+100²) =
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(1²+3²+…+99²)÷(2²+4²+…+100²) =
(1²+3²+…+99²)÷(2²+4²+…+100²) =
(1²+3²+…+99²)÷(2²+4²+…+100²) =
1²+2²+3²+...+n²=n(n+1)(2n+1)/6
1^2+3^2+5^2+.+(2n-1)^2 = n(2n+1)(4n+1)/3-2n(n+1)(2n+1)/3=n(2n+1)(2n-1)/3
所以1^2+3^2+5^2+.+(99)^2=50*101*99/3=166650
1+1²+3²+…+99²+2²+4²+…+100²=100*101*201/6=338350
2²+4²+…+100²=338350-166650=171700
(1²+3²+…+99²)÷(2²+4²+…+100²) =166650/171700=166650/17170=165/170=33/34
其实只要知道1²+2²+3²+.+n²=n(n+1)(2n+1)/6 就行
2²+4²+…+100²=4(1²+2²+…+50²)=4*50*51*101/6=171700
1²+2²+…+100²=338350
1²+3²+…+99²=338350-171700=166650
结果166650/171700=33/34