Posts for September 2024

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25-09-2024Brahmagupta-Fibonacci identity
24-09-2024Proofs of ∑k<n. 2ᵏ = 2ⁿ-1
19-09-2024Proofs of "∑i<n. i = n(n-1)/2"
12-09-2024Proofs of "If p > -1, then (1+p)ⁿ ≥ 1+np"
10-09-2024Proofs of 0³+1³+2³+3³+···+n³ = (n(n+1)/2)²
09-09-2024Proofs of a+aq+aq²+···+aqⁿ = a(1-qⁿ⁺¹)/(1-q)
07-09-2024Proofs of a+(a+d)+(a+2d)+···+(a+nd)=(n+1)(2a+nd)/2
05-09-2024Proofs of "0+1+2+3+···+n=n(n + 1)/2"
04-09-2024If f is continuous at a and the limit of u(n) is a, then the limit of f(u(n)) is f(a)
03-09-2024If x is the limit of u and y is an upper bound of u, then x ≤ y
02-09-2024If (∀ ε > 0, y ≤ x + ε), then y ≤ x