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DaniilM [7]
3 years ago
11

Find the sum of 1 + 3/2 + 9/4 + …, if it exists.

Mathematics
1 answer:
zmey [24]3 years ago
3 0

Answer:

Option (4)

Step-by-step explanation:

Given sequence is,

1+\frac{3}{2}+\frac{9}{4}..........

We can rewrite this sequence as,

1+\frac{3}{2}+(\frac{3}{2})^2.............

There is a common ratio between the successive term and the previous term,

r = \frac{\frac{3}{2}}{1}

r = \frac{3}{2}

Therefore, it's a geometric sequence with infinite terms. In other words it's a geometric series.

Since sum of infinite geometric sequence is represented by the formula,

S_{n}=\frac{a}{1-r}  , when r < 1

where 'a' = first term of the sequence

r = common ratio

Since common ratio of the given infinite series is greater than 1 which makes the series divergent.

Therefore, sum of infinite terms of a series will be infinite Or the sum is not possible.

Option (4) will be the answer.

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