posloupnosti:

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square limit:
   __n__
  |     ²²
 n|   ²²²² n      why S of triangle(n*n)/s of square(n*n)= 1/2 ?
  | ²²²²²²
  ²²²²²²²²
     n

because:
        / 1 + 2 + 3 + ... + n \
  lim  ( --------------------- ) = 1/2
 n->inf \         n^2         /



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cubic limit:
           n
       /²²²²²²²²
      //     /²² n
     / ²²²²²² ²²      why V of pyramid(n*n*n)/V of cube(n*n*n)= 1/3 ?
    | /   /²² ²²
    | ²²²² ²²/ /
    |/ /²²/   /n
     ²²/_____/

because:
        / 1 + 2^2 + 3^2 + ... + n^2 \
  lim  ( --------------------------- ) = 1/3
 n->inf \         n^3               /

...           n
          /²²²²²²²²
         //____ /²² n
        //____ / ²²
       //     /| ²²
      / ²²²²²² |/ /
     / /__ /²² / /   why V of pyramid^2(n*n*n)/V of cube^2(n*n*n)= 1/4 ?
    | /   / ²²/ /
    | ²²²² /   / n^2
    |/ /²²/   /
     ²²/_____/

        / 1 + 2^3 + 3^3 + ... + n^3 \
  lim  ( --------------------------- ) = 1/4
 n->inf \         n^4               /

        / 1 + 2^4 + 3^4 + ... + n^4 \
  lim  ( --------------------------- ) = 1/5
 n->inf \         n^5               /



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        /                      \
  lim  ( 1/1 + 1/2 + ... + 1/n  ) = +inf.
 n->inf \                      /

        /                                 \
  lim  ( 1/1 + 1/2^2 + 1/3^3 + ... + 1/n^n ) = 1.291285997
 n->inf \                                 /

        /                                 \
  lim  ( 1/1 + 1/2^2 + 1/3^2 + ... + 1/n^2 ) = 1.64493405, @n=10^8
 n->inf \                                 /

        /                                 \
  lim  ( 1/1 + 1/2^3 + 1/3^3 + ... + 1/n^3 ) = 1.20205690, @n=5*10^7
 n->inf \                                 /