Mathematical induction middle level exercise

0:00 Exercise: 1 + 1/2 + 1/3 + ... + 1/(2^n) ≥ 1 + n/2

2:17 Exercise: 1*1!+2*2!+...n*n!=(n+1)!-1

3:07 1+1/2^2+1/3^2....less than 2-1/n

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Probability and discrete mathematics:

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Probability interview questions:

https://www.youtube.com/watch?v=qphhG_1rWf8&list=PLg9w7tItBlZtI1eM6znfyDEaqQtUx5b

Probability theory:

https://www.youtube.com/watch?v=8s-nyRLBsDo&list=PLg9w7tItBlZsvciKHBx8lXXnCtQ7Ou4cV

Complex analysis:

https://www.youtube.com/playlist?list=PLg9w7tItBlZsYfYG6dUISItqsSRSXaX4B

Combinatorics:

https://www.youtube.com/playlist?list=PLg9w7tItBlZvQt0YNfCqcULzrPme2ai7K

additive combinatorics:

https://www.youtube.com/playlist?list=PLg9w7tItBlZseUrmXgf_2yc2NI_obVUhB

微積分 高等微積分 代數

Calculus and advanced mathematics (abstract algebra):

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Real analysis

https://www.youtube.com/playlist?list=PLg9w7tItBlZumEJ4DacAKgstCvDHKtY63

Reduction formula in Calculus:

https://www.youtube.com/playlist?list=PLg9w7tItBlZubmhgkHoHvje1uOASnkcke

Integrals of trigonometric functions:

https://www.youtube.com/playlist?list=PLg9w7tItBlZuwEER2YvFV06ri6i1Cj3hh

(algebraic geometry)代數幾何筆記

https://www.youtube.com/playlist?list=PLg9w7tItBlZssQ4Smzgp_bk2rEszKaW0B

Linear algebra Proof:

https://www.youtube.com/playlist?list=PLg9w7tItBlZueH6LMeYzzwPMUlIaRhCZo

環論(ring theory):

https://www.youtube.com/playlist?list=PLg9w7tItBlZs9w4wrNAuv4oJdrt-sIWUP

Abstract Algebra:
https://www.youtube.com/playlist?list=PLg9w7tItBlZsyZ0Ri0IDPYEwDxDXjCqB0

Group theory (群論):
https://www.youtube.com/playlist?list=PLg9w7tItBlZu4Qkxz2WSk4eYZmDAC8ZY0

Galois theory:
https://www.youtube.com/playlist?list=PLg9w7tItBlZsepuNJ3tOnG238M03KrKaG

數論跟其他:

number theory and others:

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Riemann Zeta functions:

https://www.youtube.com/playlist?list=PLg9w7tItBlZu4ncqL53iPd1GmwKq8yYoM

Math related to pi:

https://www.youtube.com/playlist?list=PLg9w7tItBlZuzFft3Y5h1LRaNvAv7ruKe

Number theory:

https://www.youtube.com/playlist?list=PLg9w7tItBlZvGgPYrFxfGWaQgQBrLOOws

Set Theory:

https://www.youtube.com/playlist?list=PLg9w7tItBlZsDqBUL-CIHcVVBs9EODL_J

High school math & AP calculus:
https://www.youtube.com/playlist?list=PLg9w7tItBlZv165XaBIyj03q3WSMMUqDo

Solving polynomial equation:

https://www.youtube.com/playlist?list=PLg9w7tItBlZsheN8dz8LLPy99AaLb7_-7

工程數學 Engineering Mathematics:

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Laplace transformation:

https://www.youtube.com/playlist?list=PLg9w7tItBlZty21VgNOrLTKg3BM1sFmFE

differential equation:

https://www.youtube.com/playlist?list=PLg9w7tItBlZukQ1yQXKXPo4ZN2yMHwvf1

0xab3acdec0919be9d429baf2190de2e2a4a384c7e

Legendre polynomial:

https://www.youtube.com/playlist?list=PLg9w7tItBlZvG3Ju8YUxEct1tawePe_ZA

Complex analysis:

https://www.youtube.com/playlist?list=PLg9w7tItBlZsYfYG6dUISItqsSRSXaX4B

Gamma Function:

https://www.youtube.com/playlist?list=PLg9w7tItBlZvKhQHLzaULPNtZH7mYNIf9