What is the limit of the sequence an=(n^2-n+7)/(2n^3+n^2) ?
n tends to infinite
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We'll force the factor n^2 to numerator and we'll get:
lim an = lim n^2*(1 - 1/n + 7/n^2)/(2n^3+n^2)
We'll force the factor n^3 to denominator and we'll get:
lim an = lim n^2*(1 - 1/n + 7/n^2)/n^3*(2 + 1/n)
lim an = lim (1 - 1/n + 7/n^2)/n*(2 + 1/n)
The limits of the sequences 1/n , 7/n^2 converge to zero, therefore we'll get:
lim an = 1/2*infinite
lim an = 1/infinite = 0
If n approaches to infinite, the given sequence (an) converges to zero.
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