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Find the sum of the first 20 terms of each sequence: 1,2/3,4/9,8/27,16/81

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Final answer:

The sum of the first 20 terms of the given sequence is approximately 2.99998.

Step-by-step explanation:

To find the sum of the first 20 terms of the given sequence, we can use the formula for the sum of a geometric series.

The formula is: Sum = a(1 - r^n) / (1 - r)

Where 'a' is the first term, 'r' is the common ratio, and 'n' is the number of terms.

In this case, the first term is 1 and the common ratio is 2/3.

Plugging these values into the formula, we get:

Sum = 1(1 - (2/3)^20) / (1 - 2/3)

Simplifying the expression:

Sum = 1 - (2/3)^20 / (1/3)

Finally, calculating the sum:

Sum = 3(1 - (2/3)^20)

So the sum of the first 20 terms of the given sequence is approximately 2.99998.

User Rmannn
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