Question

prove by PMI 1+4+7+ _ _ _ _ + (3n-2) = n(3n-1) /2​

Answer 1

Answer:

Step-by-step explanation:

p(1)=3×1-2  1×(3×1-1)/2

      =1         =1

ie p(1) is true

assume p(k) is true

p(k)=1+4+7.... 3k-2=k(3k-1)/2

prove that p(k+1) is true

p(k+1)=1+4+7.........3(k+1)-2

         =k(3k-1)/2+3(k+1)-2

          =(3k^2-k)/2+3k+3-2

           =(3k^2-k)/2+3k+1

            =[(3k^2-k)+2(3k+1)] /2

            =[(3k^2-k)+(6k+2)]/2

            =(3k^2+5k+2)/2

by factorising

            =(k+1)(3k+2)/2

which can be written as

            = [(k+1)(3(k+1)-1)]/2

ie p(k+1) is true

therefore p(n) is true