Question

Write the sum using summation notation, assuming the suggested pattern continues.

2 - 12 + 72 - 432 + ...

Answer 1

\[\sum_{x=0}^{\infty}\left( 2 \right)\left( -6 \right)^{x}\]

Answer 2

All good now, @tholn ?

Answer 3

thx man!!!

Answer 4

Good luck to you in all of your studies and thx for the recognition! @tholn

Answer 5

uw!

Answer 6

It's becaue (-6)^x will alternate signs. @Loser66

Answer 7

And it will start at 1, then -6, then 36, then -216. And each is multiplied by 2. @Loser66

Answer 8

It's too fundamental. the "-" in the ( ) will provide alternation.

Answer 9

The whole series, each term is multiplied by 2, so the "2" really could have gone outside the summation notation. np.

Answer 10

One last thing. The power of 6 or -6 is seen by dividing a term by the previous one. That's the real key.

Answer 11

ok, flexibility, too.

Answer 12

So with those 3 things, and that's all there really is: 1) each term multiplied by 2, 2) power of 6, and 3) alternating. That's all there is to it.