4
$\begingroup$

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.

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

$\endgroup$

3 Answers 3

10
$\begingroup$

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

$\endgroup$
1
$\begingroup$

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

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

$\endgroup$
1
$\begingroup$

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.