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▪Addition of power series :
addition of power series as a single power series is a tool which is used in solution of differential equation by power series

▪power series (in one variable) is an infinite series of the form
Infinity
£ cn(x)^n=c0+c1x+c2x^2+c3x^3+...
n=0

where cn represents the coefficient of the nth term and c is a constant. cn is independent of x and may be expressed as a function of n .
▪Power series are useful in analysis since they arise as Taylor series of infinitely differentiable functions. In fact, Borel's theorem implies that every power series is the Taylor series of some smooth function.

In many situations c (the center of the series) is equal to zero, for instance when considering a Maclaurin series. In such cases, the
These power series arise primarily in analysis, but also occur in combinatorics as generating functions (a kind of formal power series)
▪Hope so you have understand it.
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