Algebra

Step 1: Recognize the infinite geometric series in the exponent.
The exponent is . This is an infinite geometric series with the first term and the common ratio .
Step 2: Determine the condition for the convergence of the geometric series.
For an infinite geometric series to converge, , so , which means .
Step 3: Find the sum of the infinite geometric series.
The sum is .
Step 4: Substitute the sum back into the original equation.
Step 5: Solve for .
Step 6: Find the values of in the interval that satisfy .
For , . For , .
Step 7: Count the number of solutions.
There are 4 distinct solutions.