1. Should know some common ones:
Summations
Should know some common ones:
Arithmetic
Geometric
if x  1
if |x| < 1

2. ? Summations Should know some common ones:
Harmonic
Telescoping
How to solve following as telescoping sum? ?

3. Summations Combine known summations with differentiation, e.g.,
if |x| < 1
Have:
Differentiate each side:
if |x| < 1
Use algebra:
if |x| < 1
Similarly, can combine with integration.
Remember calculus?

4. Bounding is often easier & sufficient, e.g.,
Summations
Bounding is often easier & sufficient, e.g.,
With arithmetic sum, trivial:
To prove:

5. Can bound/approximate by integrals, e.g.,
Summations
Can bound/approximate by integrals, e.g.,
To prove: 1 2 3 … 4
y=1/(x+1)
y=1/x