Sequence Limit
Find the limit of a Sequence at infinity : `lim_(n -> +oo) a_n`
How to use this calculator ?
Follow the same guidelines as in this calculator Sequence value.
Examples
- Find the limit of `a_n = (4*n)/sqrt(n+1)` at infinity ?
Réponse : +oo
- Calculate `lim_(n -> +oo)(4*n^2+3*n-1)/(n^2+1)`
Answer : 4
- Calculate `a_n` limit at infinity with `a_n = log(n)/n`
Answer : 0
Limit determinate forms
We note:p (as positive) a non-zero positive real number,
n (as negative) a non-zero negative real number,
q (a non-zero number with undeterminated sign),
`+oo`, positive infinity,
`-oo`, nagative infinity,
`oo`, infinity (with undefined sign).
Determinate forms: addition and subtraction
`+oo+oo = +oo` | `-oo-oo = -oo` |
`q + (+oo) = +oo` | `q + (-oo) = -oo` |
`+oo. +oo = +oo` | `-oo. -oo = +oo` |
`p. (+oo) = +oo` | `n. (+oo) = -oo` |
`p. (-oo) = -oo` | `n. (-oo) = +oo` |
`(+oo)/p = +oo` | `(+oo)/n = -oo` |
`(-oo)/p = -oo` | `(-oo)/n = +oo` |
`q/oo = 0` | `0/oo = 0` |
`0^(+oo) = 0` | `0^(-oo) = oo` |
Limit indeterminate forms
`0/0` |
`oo/oo` |
`+oo - oo` |
`oo/oo` |
`0. oo` |
`0^0` |
`oo^0` |
`1^oo` |
See also
Sequence Value given index
Sequence Calculators
Math Calculators