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मूल्यांकित कीजिए : ((n+3)!)/(n!)...

मूल्यांकित कीजिए : `((n+3)!)/(n!)`

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Find n if. ((n!) / (3!(n - 3)!)) / ((n!) / (5!(n - 5)!)) = 5 / 3

Solve for n : ((2n)!)/( 3!( 2n-3) !) : ( n!)/( 2!( n-2)!) = 44 : 3

lm_ (n rarr oo) ((1 ^ (3)) / (n ^ (4)) + (2 ^ (4)) / (n ^ (4)) + (3 ^ (3)) / (n ^ (4)) + ...... + (n ^ (3)) / (n ^ (4)))

If n in N and Delta_ (n) = det [[n!, (N + 1)!, (N + 2)! (N + 1)!, (N + 2)!, (N + 3)! ( n + 2)!, (n + 3)!, (n + 4)!]] then lim_ (n rarr oo) ((3 ^ (n ^ (3)) - 5) Delta_ (n)) / (Delta_ (n + 1)) equals