a 2 - b 2 = (a +b)(a - b) 1/4 1 + 1/4 2 + 1/4 3 + 1/4 4 + ... = 1/3 1/3 + 1/3 2 + 1/3 3 + 1/3 4 + ... = 1/2 1/2 1 + 1/2 2 + 1/2...
a2 - b2 = (a +b)(a - b)
1/41 + 1/42 + 1/43 + 1/44 + ... = 1/3
1/3 + 1/32 + 1/33 + 1/34 + ... = 1/2
1/21 + 1/22 + 1/23 + 1/24 + ... = 1
1 + 3 + 5 + ... + (2n − 1) = n2
a2 + b2 = c2
x2 + ax = (x + a/2)2 - (a/2)2
(x + 1)2 = (x + 1)(x + 1)
= x2 + x + x + 1
= x2 + 2x + 1
(a + b)2 + (a - b)2 = 2(a2 + b2)
1 + 2 + 3 + ... + n = (n(n+1))/2
Bônus:
Fonte: Bill The Lizard, Math Made Visual, Proofs Without Words
