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        prove:-
[x/n]+[x+1/n]+.................+[x+n-1/n]=[x]
where n belongs to N
7 years ago

Jitender Singh
IIT Delhi
158 Points
										Ans:$[\frac{x}{n}]+[\frac{x+1}{n}]+[\frac{x+2}{n}] + .......... + [\frac{x+n-1}{n}] = [x]$Let$[x] = nN$$nN$N<\frac{x}{n}$N+\frac{1}{n}<\frac{x+1}{n}$N+\frac{2}{n}<\frac{x+2}{n}Similarly upto nth term,$N+\frac{n-1}{n}<\frac{x+n-1}{n}$[\frac{x}{n}]+[\frac{x+1}{n}]+[\frac{x+2}{n}] + .......... + [\frac{x+n-1}{n}] = N + N+........N = nN = [x]$Thanks & RegardsJitender SinghIIT DelhiaskIITians Faculty

3 years ago
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