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Basic real analysis
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F
Finding an interval for rational numbers with a high denominator
H
How to bound a sum of infinitely many positive real numbers
How to prove conditional convergence
I
I have a problem about an infinite sum
If you want to calculate an infinite sum exactly, relate it to coefficients associated with some function
T
To calculate an infinite sum exactly, try antidifferencing
To construct a function with several local constraints, start with simple cases and build from there
To evaluate an integral, differentiate under the integral sign
To optimize a sum try making the terms roughly equal in size
To prove that a sequence converges, find one or more convergent subsequences
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Littlewood-Paley heuristic for derivative
Geometric view of Hölder's inequality
Diagonal arguments
Finding an interval for rational numbers with a high denominator
Try to prove a stronger result
Use self-similarity to get a limit from an inferior or superior limit.
Prove a consequence first
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