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Suppose G is the generating function for the sequence 4, 7, 10, 13, 16, 19,…, the find a generating function (in terms of G) for the sequence of differences between terms.

Suppose G is the generating function for the sequence 4, 7, 10, 13, 16, 19,…, the find a generating function (in terms of G) for the sequence of differences between terms. Correct Answer (1−x)G−4/x

(1−x)G = 4 + 3x + 6x2 + 9x3 +⋯ which can be accepted. We can compute it like this: 3 + 6x + 9x2 + ⋯ = (1−x)G−4/x.

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S1:For decades, American society has been calling a melting pot.
P :Differences remained - in appearence, mannerisms, customs, speech, religion and more.
Q :The term has long been a cliche and half-truth.
R :But homogenisation was never acheived.
S :Yes, immigrants from diverse cultures and traditions did cast off vestiges of their native lands and become almost imperceptibly woven in to the American fabric.
S6:In recent years, such differences accentuated by the arrival of immigrants from Asia and other parts of the world in the United States - have become something to celebrate and to nurture.

The Proper sequence should be:
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