Question 438225
To prove a statement by mathematical induction we use three steps:

Step 1. We prove that the statement is true for n=1.

{{{9=9*1(1+1)/2}}} => {{{9=18/2}}} => {{{9=9}}}.

Step 2. Assume that the statement is true for n=k.

 9+18+27+...+9k = 9k(k+1)/2.

Step 3.We prove that the statement is true for n=k+1.

 9+18+27+...+9k+9(k+1) = 9(k+1)(k+2)/2.

Substitute the assuming result in step 2 to the step 3 we have:

{{{9k(k+1)/2+9(k+1)=9k(k+1)2+18(k+1)/2=(k+1)(9k+18)/2=9(k+1)(k+2)/2}}}, thus 

the statement is true.