a+b+c+d is a definite series with four terms. a general term(adsbygoogle = window.adsbygoogle || []).push({}); ucan be created such that the general term only satisfies a, modification can be made by adding a term x_{1}such that the general term satisfies both a and a+b. a further modification can be made by adding the term x_{2}to u+x_{1}such that the modified general term satisfies a,a+b,a+b+c. the next modification can be made by adding the term x_{3}to u+x_{1}+x_{2}such that the modified general term satisfies a,a+b,a+b+c,a+b+c+d.

using an example of a typical series of this form, show how you would find the terms x_{1},x_{2},x_{3}such that all the conditions are satisfied.

you may use any series, analyze a few examples and hence provide a general algorithm or function that may be used to find the terms.

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# Series and analysis

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