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Sum of series using partial sum?
find the sum of the series (1/3)^n using partial sums. The sum of the series is 3/2.
how would i go about answering this question?
2 Answers
- pertubalLv 45 years ago
Hmm... i'm reading this as a million/6 + a million/12 + a million/20 + a million/30 + a million/40 two + a million/fifty six + .... i should be incorrect, yet those partial sums do not pick to something common whilst n gets fairly great. Is the priority something else? * * * * * intense-high quality pastime, Phineas! I actual neglected that.
- Ron WLv 71 decade ago
Let S_n = 1 + r + r^2 + ... + r^(n-1) + r^n
Then
r S_n = r + r^2 + ... + r^n + r^(n+1)
Subtract the second from the first:
(1 - r)(S_n) = 1 - r^(n+1)
S_n = [1 - r^(n+1)] / (1 - r)
Assume that |r| < 1; then consider
lim S_n
n→∞
