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Anna007 [38]
3 years ago
15

Find the sum of the infinite series 1/3+4/9+16/27+64/81+.... if it exists.

Mathematics
1 answer:
pshichka [43]3 years ago
6 0
9/27, 12/27, 16/27

So this is a geometric sequence as each term is 4/3 the previous term.

Since the common ration is greater than one the sum of the series diverges, it does not exist.  (The sum just keeps getting larger and larger)

For a geometric series to have a sum r^2<1

So that the normal sum....

s(n)=a(1-r^n)/(1-r)   becomes if r^2<1

s=a/(1-r)
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