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MH1812 Discrete Mathematics, NTU AY25/26 Semester 1

Reference

Course-wide formulae and identities, referred to throughout the notes below.

MF26, MF27

Binomial expansion

$$(a + b)^n = a^n + \binom{n}{1}a^{n-1}b + \binom{n}{2}a^{n-2}b + \ldots + b^n$$

Sum of GP

$$\frac{a(1 - r^n)}{1 - r}$$

Sum of AP

$$\frac{n}{2}(a_1 + a_n) = \frac{n}{2}(2a + (n - 1)d)$$

Divisibility by

• 3: Sum of digits divisible by 3
• 4: Last 2 digits divisible by 4
• 8: Last 3 digits divisible by 8
• 9: Sum of digits divisible by 9

Bell numbers, B1 = 1, B2 = 2, B3 = 5, B4 = 15, B5 = 52

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