Unit 3-Lecture1: Sum & Product

1 Sums

• Arithmetic sums
• Geometric sums
• Harmonic sums

1.1 Integral method

Theorem: let f:R+→R+ be weakly increasing function. Define

S::=∑i=1nf(i)

and

I::=∫n1f(x)dx

then

I+f(1)≤S≤I+f(n)

1.2 Asymptotically equal

Definition: For functions f,g:R→R, we say f is asymtotically equal to g iff

limx→∞f(x)g(x)=1

2 Products

Stirling’s Formula

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Reference

[1] Lehman E, Leighton F H, Meyer A R. Mathematics for Computer Science[J]. 2015.