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Summations. Arithmetic. if x 1. Geometric. if |x| < 1. Should know some common ones:. Summations. Harmonic. Telescoping. How to solve following as telescoping sum?. ?. Should know some common ones:. Summations. Have:. if |x| < 1. Differentiate each side:. if |x| < 1.
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Summations Arithmetic if x 1 Geometric if |x| < 1 Should know some common ones:
Summations Harmonic Telescoping How to solve following as telescoping sum? ? Should know some common ones:
Summations Have: if |x| < 1 Differentiate each side: if |x| < 1 if |x| < 1 Use algebra: Remember calculus? Similarly, can combine with integration. Combine known summations with differentiation, e.g.,
Summations With arithmetic sum, trivial: To prove: Bounding is often easier & sufficient, e.g.,
Summations 1 To prove: y=1/x y=1/(x+1) … 0 0 1 2 3 4 Can bound/approximate by integrals, e.g.,