`S_(n)` be the sum of n terms of the series `(8)/(5)+(16)/(65)+(24)/(325)+"......"`
The seveth term of the series is (a)`(56)/(2505)` (b)`(56)/(6505)` (c)`(56)/(5185)` (d)`(107)/(9605)`

Options

A. `(56)/(2505)`
B. `(56)/(6505)`
C. `(56)/(5185)`
D. `(107)/(9605)`

Explanation

To find the seventh term of the series given by \( S_n = \frac{8}{5} + \frac{16}{65} + \frac{24}{325} + \ldots \), we need to identify the general term \( T_n \) of the series.

### Step-by-Step Solution:

1. **Identify the General Term**:
The series appears to have a pattern in both the numerators and denominators. By examining the first few terms:
- The numerators are \( 8, 16, 24, \ldots \), which can be expressed as \( 8n \) where \( n \) is the term number.
- The denominators are \( 5, 65, 325, \ldots \). We can see that these denominators can be expressed as \( 4n^4 + 1 \).

Thus, we can write the \( n \)-th term as:
\[ T_n = \frac{8n}{4n^4 + 1} \]

2. **Calculate the Seventh Term**:
Now, we need to find \( T_7 \):
\[ T_7 = \frac{8 \times 7}{4 \times 7^4 + 1} \]

First, calculate \( 7^4 \):
\[ 7^4 = 2401 \]

Now substitute this value into the denominator:
\[ 4 \times 7^4 + 1 = 4 \times 2401 + 1 = 9604 + 1 = 9605 \]

Now substitute back into the expression for \( T_7 \):
\[ T_7 = \frac{56}{9605} \]

3. **Final Result**:
Thus, the seventh term of the series is:
\[ T_7 = \frac{56}{9605} \]

### Answer:
The correct option is (d) \( \frac{56}{9605} \).