SOLUTION: Let P (n) represent the statment 2+6+10+...+(4n-2)=2n^2 In the proof that P (n) is true for all integers n, n>1, what term must be added to both sides of P (k) to show P (k+1) f

Question 31747: Let P (n) represent the statment 2+6+10+...+(4n-2)=2n^2
In the proof that P (n) is true for all integers n, n>1, what term must be added to both sides of P (k) to show P (k+1) follows form p(k)?
(A) 4k+2
(B) P(k+1)
(C) 4k+6
(D) 4k-2
Thank you for your assistance!
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Let P (n) represent the statment 2+6+10+...+(4n-2)=2n^2
In the proof that P (n) is true for all integers n, n>1, what term must be added to both sides of P (k) to show P (k+1) follows form p(k)?
(A) 4k+2
(B) P(k+1)
(C) 4k+6
(D) 4k-2
P(K)=(4K-2)...SO WE HAVE TO ADD THE NEXT TERM THAT IS P(K+1) TO BOTH SIDES TO PROVE THE EQUALITY BY INDUCTION METHOD.
SO P(K+1)=4(K+1)-2=4K+4-2=4K+2 IS THE NUMBER WE SHOULD ADD TO BOTH SIDES ....A IS THE ANSWER.
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