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Concrete mathematics : a foundation for computer science

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50 SUMS<br />

Let’s try to recap this; in a slightly different way. Suppose we’ve been<br />

given an unknown sum that’s supposed to be evaluated in closed <strong>for</strong>m, and<br />

suppose we can write it in the <strong>for</strong>m taskcb g(k) = I.“, g(x) 6x. The theory<br />

of finite calculus tells us that we can express the answer as f(b) - f(a), if<br />

we can only find an indefinite sum or anti-difference function f such that<br />

g(x) = f (x + 1) - f(x). C)ne way to understand this principle is to write<br />

t aGk

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