Asked by Sharen
Determine whether the infinite geometric series converges. If so, find the sum
1/4+1/16+1/64+1/256....
1/4+1/16+1/64+1/256....
Answers
Answered by
Jai
The geometric sequence is
1/4 , 1/16 , 1/64 , 1/256 , ...
And the ratio is
r = 1/16 / (1/4) = 1/4
This infinite geometric sequence converges because the ratio is in the range of -1 < r < 1.
Getting the sum, we use the formula,
S = a1 / 1 - r
S = 1/4 / (1 - (1/4))
S = 1/4 / (3/4)
S = 1/3
Hope this helps~ `u`
1/4 , 1/16 , 1/64 , 1/256 , ...
And the ratio is
r = 1/16 / (1/4) = 1/4
This infinite geometric sequence converges because the ratio is in the range of -1 < r < 1.
Getting the sum, we use the formula,
S = a1 / 1 - r
S = 1/4 / (1 - (1/4))
S = 1/4 / (3/4)
S = 1/3
Hope this helps~ `u`
Answered by
Sharen
Thank you!
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