Question

Can you calculate this limit pls?

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

Answer 1

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