How to solve <munder> <mo form="prefix">lim <mrow class="MJX-TeXAtom-ORD"> n

Petrovcic2x 2022-06-22 Answered
How to solve lim n ( a 1 n + b 1 n 2 ) n
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

plodno8n
Answered 2022-06-23 Author has 17 answers
Assuming a , b > 0
We have
( a 1 n + b 1 n 2 ) n = a ( 1 + r 1 n 2 ) n ,
where r = b / a. We can write
a ( 1 + r 1 n 2 ) n = a ( 1 1 r 1 n 2 ) n = a exp [ n log ( 1 1 r 1 n 2 ) ] = a exp [ n log ( 1 1 e 1 n log r 2 ) ] = a exp [ n log ( 1 1 n log r + o ( 1 n 2 ) 2 ) ] = a exp [ n log ( 1 + 1 2 n log r + o ( 1 n 2 ) ) ] = a exp [ 1 2 log r + o ( 1 n ) ) ] a e 1 2 log r = a r 1 / 2 = a b .
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions