use mathematical induction to show that (a) 1 + 4 +7 + ...+(3n -2) = n (3n - 1)/2 for n is the element of natural numbers, n is greater than or equal to 1.(

Answer:It is true for  n=1if n=k is true then n=k+1 is also trueStep-by-step explanation:n=1:[tex]1=1(3*1-1)/2\\1=2/2\\1=1\\[/tex]       TRUEn=k:[tex]1 + 4 +7 + ...+(3k -2) = k (3k - 1)/2\\[/tex]n=k+1:[tex]1 + 4 +7 + ...+(3k -2)+ (3(k+1)-2) =k(3(k+1)-1)/2 \\[/tex]We replace the first part of the equation with our value for n=k:[tex]k (3k - 1)/2+(3(k+1)-2)=k(3(k+1)-1)/2 \\[/tex]we develop both sides of the equation to verify equality:[tex]3k^{2} /2-k/2+3k+1=(k+1)(3k+2)/2\\\\3k^{2} /2+5k/2+1=(3k^{2}+5k+2)/2\\\\3k^{2} /2+5k/2+1=3k^{2} /2+5k/2+1[/tex]       TRUE