Prove the following using the following definition of O,Big-omega,Theta, small omega
Σki=1 ?i ?i = ?(nk )??? ? > 1.
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Let f(n)=a(1)*n+a(2)*n^2+.....a(k)*n^k
Since we know n^k>=n^c for any c<=k
So,
f(n)=a(1)*n+a(2)*n^2+.....a(k)*n^k<=(a(1)+a(2)+a(3)+.....a(k))*n^k
Let c=(a(1)+a(2)+a(3)+.....a(k))
So,
f(n)<=c*n^k
So, by deifinition of Big O
f(n)=O(n^k)
Kindly revert for any queries
Thanks.
Prove the following using the following definition of O,Big-omega,Theta, small omega Σki=1 ?i ?i = ?(nk...
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