Find the limit of the sequence [a_n]=[\frac{2}{\sqrt{n^{2}+7n}-\sqrt{n^{2}+2n}}]

Emerson Barnes

Emerson Barnes

Answered question

2022-01-25

Find the limit of the sequence
[an]=[2n2+7nn2+2n]

Answer & Explanation

stamptsk

stamptsk

Beginner2022-01-26Added 23 answers

an=2n2+7nn2+2n
=2(n2+7n+n2+2n)(n2+7nn2+2n)(n2+7n+n2+2n)
=2(n2+7n+n2+2n)n2+7nn22n
=2(n2+7n+n2+2n)5n
=25(1+7n+1+2n)
Now,
limnan=limn25(1+7n+1+2n)
=25(1+1)
=45
Thus, limit of an is 45
plusmarcacw

plusmarcacw

Beginner2022-01-27Added 10 answers

finally, thanks

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