or
or
ধারাটির যোগফল হল-
The expression given in the question represents an infinite series. It starts with 1 and adds fractions where the denominators follow the powers of 3: 3, 9 (which is 32), 27 (which is 33), and so on.
This series can be expressed as:
This is a geometric series where the first term (a) is 1, and the common ratio (r) is 1/3. The formula for the sum of an infinite geometric series is:
S = a / (1 - r)
Substituting the values:
We get:
S = 1 / (1 - 1/3) = 1 / (2/3) = 3/2
Hence, the sum of the series is , which corresponds to option a. Therefore, the given answer is correct.
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