Find lim(n->infinity) (8^n + 7^n)^(1/n). Thanks!?

Question

Find lim(n->infinity) (8^n + 7^n)^(1/n). Thanks!?

Answer 1

take 8^n out

= (8^n)^(1/n) ( 1+ (7/8)^n)^(1/n)

= 8( 1+ (7/8)^n)^(1/n)

as n->infinite the 2nd part is 1 as (7/8)^n tends to zero and then (1+0)^0 tends to 1

so = 8

Answer 2

(8^n + 7^n)^(1/n) = 8[1 + (7/8)^n]^(1/n).

Now 7/8 <1 so it higher powers will tend to 0 as n tend to infinity. So the limit is 8.