Question

Help with a geometric series question? Thanks
I just learned arithmetic series now I'm moving on whooh! :) ha.

Find the sum: 10 is on top of the E, 2i is on the right side of the E, and I= 1 is on the bottom of the E.
2046
2050
1022
1024

Answer 1

Do you mean:
\( \displaystyle \sum_{i = 1}^{10} 2i \)
or
\( \displaystyle \sum_{i=1}^{10} 2^i \)
I was thinking the second, but just to be clear if you have an exponent it is more clear to write it as 2^i rather than 2i

Answer 2

The second one :)
And I'm just wondering but I'm trying to work it out and is the answer 1022?

Answer 3

what was your process to get that answer? :)

Answer 4

While the first time I did it I got -510 so that's way off and now I'm trying it again and I'm just lost.

Answer 5

N = 10, a1= 2 and r = 2? R those at least right?

Answer 6

What was the formula you were using? Just need to make sure we have the same one.

Answer 7

Sn = a1 ( 1 - r^n) / 1 - r

Answer 8

Alright.
a1 = 2 looks good to me then
r = 2 as well
N = 10 is good
so you just plug them straight in and got the answer 1022?

Answer 9

While after I got -510 I was really mad at the problem so I just multiplied 510 * 2 and it came up at. 1020. Ha

Answer 10

Aha, gotcha.
Because when you use that formula with the values you just suggested, I seem to have obtained a right answer... :p

Answer 11

a_1 (1 - r^n) / (1 - r)
2 (1 - 2^10)/ (1 - 2)

Answer 12

Is it 2046?? Cuz that's the new answer I just got

Answer 13

Looks good to me. :)

Answer 14

Yes! Finally I got the right answer! :) thank you for the help!

Answer 15

in this case, if you reaally wanted to, you could probably just calculate 2^1 + 2^2 + 2^3 + ... 2^10 on a calculator too. that would also confirm any doubts. ;x