Question
Proceed as in Example 3 to rewrite the given expression using a single power series whose general term involves $x^{k}$.$$\sum_{n=1}^{\infty} n c_{n} x^{n-1}+3 \sum_{n=0}^{\infty} c_{n} x^{n+2}$$
Step 1
We can do this by substitifying $k = n - 1$. This implies that $n = k + 1$. Substituting these into the first series, we get: $$\sum_{k=0}^{\infty} (k+1) c_{k+1} x^{k}$$ Show more…
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