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santosh kumar kurashetty Grade:
        

can you please elaborate and explain the answer for


prove n^n<=(2n)!   using mathematical induction?

6 years ago

Answers : (1)

Sudheesh Singanamalla
114 Points
										

given : n^n


to prove : n^n = 2n!


for n=1


(1^1 = 1) <= (2*1 = 1)


since it is true for n=1, for n=k


k^k <= 2*k!


assuming n=k to be true, multiplying bothsides by k we get


k^k * k^1 <= (2*k)! * k


k^k+1 <= (2*k*k) * (2*(k-1))! = 2[(k*k)*(k-1)]!


this is of the form  n^n = 2n!


 


therefore n^n = 2n!

6 years ago
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