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Question Number 162414 by HongKing last updated on 29/Dec/21
ProvetheIdentityforany(a,n)inRealNumber(1+a)⋅a[n]=a⋅a2[n2]+a2[n+12][∗]GreatestIntegerFunction
Answered by mindispower last updated on 31/Dec/21
n∈[2k,2k+1[[n]=2k(1+a).a2k=a.a2k+a2k=(1+a).a2ktruen∈[2k−1,2k][n]=2k−1[n2]=k−1[n+12]=k(1+a).a2k−1=?a.a2(k−1)+a2k=a2k−1+a2k=a2k−1(1+a)True(1+a).a[n]=a.a2[n2]+a2[n+12]
Commented by HongKing last updated on 31/Dec/21
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