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3 years ago

Find the sum of the series 9+3+1+........+1/27

Mathematics

1 answer:

Elina [12.6K]3 years ago

4 0

Answer:

364/27

Step-by-step explanation:

9, 3, 1, ... is a geometric sequence with common ratio r = 1/3.

The nth term is a1rn-1.

If a1rn-1 = 1/27, then 9(1/3)n-1 = 1/27

32(3-1)n-1 = 3-3

3231-n = 3-3

33-n = 3-3

3-n = -3

n = 6

The sum, Sn, of the first n terms of a geometric sequence is given by Sn = a1(1 - rn) / (1 - r).

So, 9 + 3 + 1 + ... + 1/27 = S6 = 9(1 - (1/3)6) / (1 - 1/3)

= 9(1 - 1/729) / (2/3)

= (27/2)(728/729) = 364/27

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