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Question

2 + 6 + 18 + ... + 2 * 3 to n-1 power = 3 to n-1 power

use mathematical induction to prove the statement are true for every positive integer n.

Answer 1

If I am correct, the sum is equals to 3^n - 1 (not 3 ^(n-1))

To use math induction, you first prove that for a value of n=1, this is true.

2 = 3 -1 = 2

and then prove that if it is true for n, then it is true for n+1

2 + 6 + 18 ... 2*3^(n-1) + 2*3^n = 3^n - 1 + 2*3^n
= (1+2)*3^n - 1 = 3 * 3^n -1 = 3^(n+1) - 1

Hence the statement is true

Answer 2

Are you sure that you have that right ?

Unless I am missing something you are asked to prove that

a list of numbers plus 2 * 3 to n-1 power = 3 to n-1 power

that doesn't make sense to me !

Answer 3

Norman is right, except you do not prove it is true for n, you assume that it is true for n then prove it is true for n+1.