What is the sum of the geometric series 2^0+2^1+2^2+2^3+2^3+2^4+--+2^9?

A: 1,023
B: 511
C: 2,407
D: 1,012

Question

What is the sum of the geometric series 2^0+2^1+2^2+2^3+2^3+2^4+--+2^9?

A: 1,023
B: 511
C: 2,407
D: 1,012

hartnn · Answer

do you know the formula of sum of geometric sequence

hartnn · Answer

ever seen this formula ?
$\large S_n= a_1 \dfrac{r^n-1}{r-1}$
?

anonymous · Answer

Yes

hartnn · Answer

can you find a1 ? r ? n ?

hartnn · Answer

or know what they are ?

hartnn · Answer

a1 = 1st term = .... ?
r = common ratio = 2^1/2^0 = 2^2/2^1 =... ? 
can you find these ?

anonymous · Answer

2^0 is the. 1st term

hartnn · Answer

correct! :)
a1 = 2^0 =1 
what about r ?

anonymous · Answer

Like 2^0, 2^1,2^3

hartnn · Answer

r = common ratio
it is the number that you multiply to current term to get next term
so, here r = 2^1/2^0 = ... ?

anonymous · Answer

2?

hartnn · Answer

correct! 
r= 2 :)
from 2^0 to 2^9 , there are 10 terms, right ?
so, n=10
any doubts till here ?

anonymous · Answer

Nope

hartnn · Answer

good,so plug these in that formula and simplify ...
can you or need help with that ?

anonymous · Answer

I got it and the answer was A, thank you

hartnn · Answer

thats correct! 
S = r^10-1 = 1024 -1 = 1023 :) 
good :)

hartnn · Answer

and since you're new here,
$\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} $

anonymous · Answer

Thank you

hartnn · Answer

welcome ^_^