The expression you’ve shared appears to be a summation with some parts unclear. I'll interpret it as follows:

$\sum_{n=1}^{\infty} \left( n \cdot 2^{n-1} \cdot x^{n-1} \right)$

Is this correct? If not, please clarify or upload a clearer image, and I can assist further.

For now, here’s a solution outline based on my interpretation:

1. Rewrite the expression in standard summation form.
2. Identify if there is a geometric or power series form.
3. Use known summation formulas or calculus methods if necessary to solve.
4. Interpret the series convergence properties if the upper limit is infinity.

Would you like detailed steps for solving this type of summation, or have I interpreted it correctly?

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Related Questions:

1. How do I determine convergence for a series with variable $x$?
2. What are standard formulas for summing geometric or power series?
3. How does the series convergence change with respect to $n$ in infinite limits?
4. How can we use calculus to evaluate infinite series?
5. What happens if the exponent of $x$ or $n$ changes in the summand?

Tip:

For complex series, first simplifying the general term can often reveal patterns or known series forms, making it easier to evaluate or estimate convergence.