Find the sum to infinity to the following series 3 + 2 + 43 4 3 + 89 8 9 + 1617 16 17 + .....

Find the sum to infinity to the following series 3 + 2 + $\frac{4}{3}$ + $\frac{8}{9}$ + $\frac{16}{17}$ + .....

Answer Details

To find the sum to infinity of this series, we need to determine if it is a converging or diverging series. We can do this by finding the common ratio between each term. The common ratio between the second and first term is 2/3. The common ratio between the third and second term is 4/3. The common ratio between the fourth and third term is 8/9, and so on. We can see that the common ratio is less than 1, so the series is converging. Therefore, we can use the formula for the sum of an infinite geometric series: S = a/(1 - r) where S is the sum, a is the first term, and r is the common ratio. In this case, the first term is 3 and the common ratio is 2/3. So, plugging these values into the formula, we get: S = 3/(1 - 2/3) = 3/(1/3) = 9 Therefore, the sum to infinity of this series is 9. So, the answer to the question is option (D) 9.