Find the sum of infinite term of the following series : `16+8+4…oo`

Explanation

To find the sum of the infinite series \( 16 + 8 + 4 + \ldots \), we can recognize that this series is a geometric series.

### Step-by-step Solution:

1. **Identify the first term (a) and the common ratio (r)**:
- The first term \( a \) of the series is \( 16 \).
- To find the common ratio \( r \), we can divide the second term by the first term:
\[ r = \frac{8}{16} = \frac{1}{2} \]
- We can also check the ratio between the third term and the second term:
\[ r = \frac{4}{8} = \frac{1}{2} \]
- Thus, the common ratio \( r \) is \( \frac{1}{2} \).

2. **Check if the series is convergent**:
- A geometric series converges if the absolute value of the common ratio \( |r| < 1 \). Here, \( r = \frac{1}{2} \), which satisfies this condition.

3. **Use the formula for the sum of an infinite geometric series**:
- The formula for the sum \( S \) of an infinite geometric series is given by:
\[ S = \frac{a}{1 - r} \]
- Plugging in the values we found:
\[ S = \frac{16}{1 - \frac{1}{2}} = \frac{16}{\frac{1}{2}} = 16 \times 2 = 32 \]

4. **Conclusion**:
- The sum of the infinite series \( 16 + 8 + 4 + \ldots \) is \( 32 \).

### Final Answer:
The sum of the infinite series is \( 32 \).