Question 144244
In using mathematical induction to prove 8+10+12+...+(2n+6) = n^2+7n, the 
P(k+1) statement is 8+10+12+...+(2k+6) + 2(k+1)+ 6 = (k+1)^2+7(k+1)
---------------------
---------
Assume P(k)= 8 + 10 + ...+2k+6 = k^2+7k is true

Show that P(k+1) = 8+10+12+...+(2k+6) + (2(k+1)+6) = (k+1)^2 + 7(k+1) 
Substituting on the left side you get:
P(K) +2(k+1) + 6 
= k^2+7k + 2(k+1)+6
= k^2+ 2x+8 + 7k
= k^2 + 2x + 1 + 7k+7
= (k+1)^2 + 7(k+1)
--------
So the form is true for all k.
================
Cheers,
Stan H.