- #1
shan
- 57
- 0
We were given the series:
1/2^6 - 1/2^8 + 1/2^10 - 1/2^12 + ...
And asked to find the general term, an, which I worked out to be (-1)^(n+1)/2^(4+2*n).
To see if it converged, I used the alternating series test and found that it converged ie the lim as n tends to infinity = 0 and the absolute values of the terms are decreasing.
The last part of the question asks for the sum of the series but I don't know how to find it. I searched on the internet but only found the alternating series estimate theorem which we haven't been taught and don't know how to use
1/2^6 - 1/2^8 + 1/2^10 - 1/2^12 + ...
And asked to find the general term, an, which I worked out to be (-1)^(n+1)/2^(4+2*n).
To see if it converged, I used the alternating series test and found that it converged ie the lim as n tends to infinity = 0 and the absolute values of the terms are decreasing.
The last part of the question asks for the sum of the series but I don't know how to find it. I searched on the internet but only found the alternating series estimate theorem which we haven't been taught and don't know how to use