prove by pmi

prove by pmi PRINCIPLE 'OF MATæ e 7 Pro e that 3 n 12 +22 + > 3

Dear Student ,
Please find below the solution to the asked query :

Let Pn be the given statement,Pn: 12+22+ ... +n2 > n33 , nNFor n=112>1331>13It is true.Let us assume that it is also true for n=k 12+22+ ... +k2 > k33Now,For n=k+1 12+22+ ... +k2 +k+12>k33+k+12                              Since  12+22+ ... +k2 > k33 =k3+3k2+6k+33=k3+3k2+3k+1+3k+23=k3+3k21+3k12+12+3k+23=k+13+3k+23>k+133So , it is also true for n=k+1.Hence, By PMI Pn is true for all nN .
Hope this information will clear your doubts about the topic .
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible .


  • 1
What are you looking for?