| (a−b)(a+b) | ||
(a−b)= | ||
| a+b |
| 4 n2 + n + 1 − 4n2 | ||
an = √4 n2 + n + 1 − 2 n = | = | |
| √4 n2 + n +1 + 2n |
| n + 1 | ||
= | ; dzielimy licznik i mianownik przez n | |
| √4n2 + n +1 + 2n |
| 1 + 1n | ||
an = | ||
| √4 + 1n + 1n2 + 2 |
| 1 + 0 | 1 | |||
lim an = | = | |||
| √4 + 0 + 0 + 2 | 4 |
| a2−b2 | ||
a−b = | ||
| a+b |
| a2−b2 | ||
lim √4n2+n+1 − 2n = lim a−b = lim | = lim | |
| a+b |
| (√4n2+n+1)2−(2n)2 | 4n2+n+1−4n2 | |||
= lim | = lim | |||
| √4n2+n+1+2n | √4n2+n+1+2n |
| n+1 | n(1+1n) | |||
= lim | = lim | |||
| √4n2+n+1+2n | √n2(4+1n+1n2) +n*2 |
| n(1+1n | ||
= lim | ||
| n*√4+1n+1n2+n*2 |
| n(1+1n) | 1+1n | |||
= lim | = | |||
| n*(√4+1n+1n2+2) | √4+1n+1n2+2 |
| 1+0 | 1 | 1 | 1 | |||||
= | = | = | ||||||
| √4+0+0+2 | √4+2 | 2+2 | 4 |
| 5^2 | 52 |
| 2^{10} | 210 |
| a_2 | a2 |
| a_{25} | a25 |
| p{2} | √2 |
| p{81} | √81 |
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