Mathematical Induction Question (1 Viewer)

[ShawnG]

Hi I dont usually ask for help but Ive been stuck on this question for a while

2 + 5 + 8 ...+ (3n-1) = n/2(3n+1)

Thanks for the help in advance.

 

[Trebla]

n = 1
LHS = 2
RHS = 1(4)/2 = 2
LHS = RHS, so statement is true for n = 1
Assume the statement is true for n = k
2 + 5 + 8 ...+ (3k - 1) = k(3k + 1)/2
Required to prove statement is true for n = k + 1
2 + 5 + 8 ...+ (3k + 2) = (k + 1)(3k + 4)/2
LHS = 2 + 5 + 8 ...+ (3k - 1) + (3k + 2)
= k(3k + 1)/2 + (3k + 2)
= (3k² + k + 6k + 4)/2
= (3k² + 7k + 4)/2
= (3k + 4)(k + 1)/2
= RHS
If the statement is true for n = k, it is also true for n = k + 1
Since the statement is true for n = 1, it follows by induction that it is true for all positive integers n