# Real analysis

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Using the definition of convergence of a sequence

show that the following sequences converge to the proposed limit: 1-lim 1/(6n^2+1)=0

2-lim 2/sqrt[n+3]=0

3-lim (3n+1)/(2n+5)=3/2

https://brainmass.com/math/real-analysis/real-analysis-25454

#### Solution Preview

1-

Let epsilon> 0 and let N be a natural number such that 1/(6N^2)< epsilon. Then if n>= N we will have:

|1/(6n^2+1)|< |1/(6n^2)|<= |1/(6N^2)|< epsilon

And that is what we were ...

#### Solution Summary

This uses the definition of convergence of a sequence to show that sequences converge to the proposed limits.

$2.49