How does $3^n-1+2 \cdot 3^n$ evaluate to $3^{n+1}-1$?

Question

Can anybody here help me with this simple problem? I've been thinking about this for half an hour and I am not able to come to a solution.

score 10 · Accepted Answer · answered Mar 20 '13 at 13:24

10

Note that $$3^{n+1} = 3 \cdot 3^n = (1+2)3^n = 3^n+2\cdot 3^n$$

answered Mar 20 '13 at 13:24

Stefan

Inceptio · Answer 2 · 2013-03-20T13:34:01.953

1

Hint: $(1+2)3^n-1 \implies 3^{n-1}-1$. Grouping terms.

edited Mar 20 '13 at 13:34

answered Mar 20 '13 at 13:27

Inceptio

score 1 · Answer 3 · edited Mar 20 '13 at 13:33

1

$3^n -1 + 2\cdot3^n$ = $3\cdot3^n -1$

= $3^{n+1}-1 $

edited Mar 20 '13 at 13:33

Américo Tavares

answered Mar 20 '13 at 13:31

lsp

3 Answers3