Find the effective force constant in the situation when infinite number of springs with springs constant k 2k, 4k, 8k, …. Respectively are connected in series.

Explanation

To find the effective force constant when an infinite number of springs with spring constants k, 2k, 4k, 8k, ... are connected in series, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Spring Constants**: The spring constants of the springs are given as k, 2k, 4k, 8k, and so on. This can be expressed as:
- \( k_1 = k \)
- \( k_2 = 2k \)
- \( k_3 = 4k \)
...