Use summation given below to find a function that it represents

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Use summation given below to find a function that it represents

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[\sum _{n=1}^{\infty } \text{nx}^n\]
\[x/(x-1)^2\]
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yeah, sorry, busy busy, here it goes
\[\sum_{1}^{∞}n x ^{n} = x * \sum_{1}^{∞}n x ^{n-1} = x * d/dx[\sum_{1}^{∞} x ^{n}] = x * d/dx[1/(1-x)] = x/[(1-x)^{2}]\] Excuse me for the poor formating but the website doesn't offer much of choice. The star (*) stands for multiplication. Thanks.
Hey there's one catch: correct this: \[x * d/dx[\sum_{0}^{n} x ^{n}]\] Because when we differentiate, n->0 not n->1 Thanks

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