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If Di=1nn2in2+n+1n2+n2i-1n2n2+n+1andi=1nDi=56then n must be = ______

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detailed solution

7

Di=1nn2in2+n+1n2+n2i-1n2n2+n+1Write in to n-determinants and apply

i=1nDi=i=1n1nni=1n2in2+n+1n2+ni=1n2i-1n2n2+n+1 i=1nDi=nnnn(n+1)n2+n+1n2+nn2n2n2+n+1 i=1nDi=n00n2+n10n20n+1=n(n+1)n(n+1)=56n=7

 

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