Now you need to COMBINE the sums into one big sum. Be careful though, because it's easy to make mistakes with the coefficients! If you are not sure, the way to do it is to make a change on the index so that the X has the same power in each series. After that, choose the lowest common index (say n = 2 or something like that) for all the series and convert each series to that index by taking out the terms with lower indices, i.e.:
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Once you combine the series you will get some big series and since it's equal to 0, it must be equal to 0 for all x. This can only happen if all the coefficients are 0. Then set the big coefficient of the combined series to 0 and now you have a recurrence relation, which you can use to calculate the coefficients!