What is the limit of this converging sequence? (Calc 2)?

1) Divide top and bottom by n giving

(1 + (1/n))/(2 - (1/n))

Now let n->∞ giving ?

2) Do a similar thing here, divide top and bottom by √n

giving 1/((1/√n)+1) and let n->∞ giving ?

First one is 1/2. Let f(x) = sequence lim x-->infinity (x+1)/(2x-1) = 1/2

Second one is 1. Same process, let f(x) = sequence lim x---> infity [(sqrtx)/(1+sqrtx)] = 1.

This goes back to finding limits as x goes to infinity. If the largest power of x occurs both in the numerator and denominator then just take the ratio of the coefficients.

(n + 1)/(2n - 1)

Limit

1/2

Sqrt[n]/(1 + Sqrt[n])

Limit

1

It depends, what is n approaching? Assuming it's approaching infinity, the first one would be 1/2 and the second would be 1.