Can you calculate this limit pls?

lim(n->∞)((n+1)^2+5n^5+10)/((n+1)^5+2n^2+10)

1 Answer
May 28, 2018

5

Explanation:

Expand (n+1)^5 using binomial Coefficient we get the result as
lim(nrarroo) (n^2+2n+1+5n^5+10)/(C_0n^5+C_1n^4+C_2n^3+C_3n^2+C_4n+C_5n^0+2*n^2+10)

Take n^5 common from denominator and numerator and apply
limit
lim(n rarroo) (n^2/n^5+2n/n^5+1/n^5+5n^5/n^5+10/n^5)/(C_0n^5/n^5+C_1n^4/n^5+C_2n^3/n^5+C_3n^2/n^5+C_4n/n^5+C_5n^0/n^5+2*n^2/n^5+10/n^5)
And Result come 5/1