5.
f(n) = an, (n ÎN), . , , n f f(n). , f , , , , n, . , : 1, 4, 9, 16, 25,.., n2,... = { n 2}.
, , . . , + d, + 2d, + 3d,...= { + (n-1)d } : n = n-1 + d.
b, bq, bq2, bq3,...= { bqn-1 } : bn+1 = bn q.
, , . , , b, d q.
{ xn } , ( ), , , xn < M n.
{ xn } , m ( ), xn > m n.
xn > xn-1, .
xn < xn-1, .
n , .
{ xn } , .
.
. :
1, 0, -1, -2, -3,......, - ,....;
2, 4, 6,......2 n, ...;
1, 2-1, 2-2, 2-3, ., 2-n .
, , 2 .
, , 1 .
.
{ n } , ( ) N , n > N | n | > .
{ xn } , ε>0 ( ) N , n > N | xn | < ε.
|
|
1. , 1.
.
{xn} , ε > 0 N(ε), n N, n > N |xn ‒ | < ε.
{ xn } : . , xn .
:
.
ε = 0,01, . , .
N(0,0001). .
, , n = 99, | xn 1| < 0,01, n = 9999, | xn 1| < 0,0001.
, .
( ) . , , N, ( - ε, + ε), ε- .
ε , N . , ε-, . , N , ε-. , , , xn .
, . { xn } , : (: xn n, , ). , { xn } , .
{xn} , E N(E), n N(E), n > N(E) |xn| > E.
xn> 0, , xn . xn < 0, , xn .
, . , -1, 1, -1, 1,... (-1)n,... , . -1, 0, -1, -2, -3,......, - ,.... , , .