1-qn 1 1 1 1 n
1 + q + q2 + ... + qn-1 = q = 1 + + + ... + =

1-q 1�2 2�3 3�4 n(n+1) n+1
(1 + x)n e" 1 + nx x e" -1 2n-1 < n!
n+1
sin x
nx
2
sin x + sin 2x + ... + sin nx = sin x = 2kĄ

x
sin 2
2
2n

n n n
(a + b)n = anb0 + an-1b1 + ... + a0bn a, b " R
0 1 n
1/n n
A = {2n : n " N} B = {2p : p " N} C = {p - q : p, q " Q}

"
n
1
A = 5 : n " N B = {x " R : sin x e" 0} C = n + : n " N
n

p
A = : p, q " N, p < q B = {x " R : tgx = 7} C = {x " R : x2 + 3x - 8 < 0}
q

"
4n 2n
n
A = : n " N B = : n " N C = { n : n " N}
n2+1 n+1

(-1)n
n 1
A = {2-n : n " N} B = 1 + : n " N C = : n " N
k=1
n+1 2k
A, B �" R A+B = {a + b : a " A, b " B}
A, B sup(A+B) = sup A+sup B