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bionomial theorem prob
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f=R-[R]  R=I+f let F=(5 5-11)2n+1 11<55<120<55-11<10<F<1 0<f<1....(1) -1<-F<0.......(2) -1<f-F<1 ........(3)I+f-F=(5 5+11)2n+1-(55-11)2n+1=2[ c1(55)2n(11)+c3(55)2n-2(11)3+......] =2k {k is an integer} since I is an integer, f-F is also an integer f-F=0 From (3)f=FRf=RF=(5 5+11)2n+1(55-11)2n+1=(125-121)2n+1=42n+1hence Rf=42n+1 |
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