Revision as of 19:04, 6 January 2020

Memorize

These are things you need to memorize.

Order of operations: first parenthesis, then exponents, then multiplication/division/modulus, then addition and subtraction. And left to right.
Powers/exponents
- 2¹⁰ = 1024, roughly 1 thousand
- 2^a+b = 2^a * 2^b
- y^a+b = y^a * y^b
- 2^-a = 1 / (2^a)
- 2²⁰ = 1024 × 1024, roughly 1 million
- 2³⁰ = 1024 × 1024 × 1024, roughly 1 billion
Logarithms
- log_bx = y, means b^y = x, for any b > 1
- log₁₀1000 = 3
- log₂1024 = 10
- log_bx = log_cx / log_cb, for any b > 1, c > 1
- log₂10 is about 3.32
- log_b(xy) = y log_b x, for any b > 1
Formulae
- Arithmetic Sum: (1 + 2 + ... + n) = n * (n+1) / 2
- Geometric Sum: 1 + r + r² + r³ + ... + rⁿ = (rⁿ⁺¹-1) / (r-1)

@@ Line 18: / Line 18: @@
 * ''Formulae''
 ** Arithmetic Sum: (1 + 2 + ... + n) = n * (n+1) / 2
-** Geometric Sum: 1 + r + r<sup>2</sup> + r<sup>3</sup> + ... + r<sup>n</sup> = (r<sup>n+1)-1) / (r-1)
+** Geometric Sum: 1 + r + r<sup>2</sup> + r<sup>3</sup> + ... + r<sup>n</sup> = (r<sup>n+1</sup>-1) / (r-1)