Does this answer make sense

Question

(1/1+√3) + (1/√3 + √5) + (1/√5+√7) + ... + (1/(√(2n-1)) + (√(2n+1)) = 300

 

1/[sqrt(2n - 1) + sqrt(2n + 2)] = [sqrt(2n - 1) - sqrt(2n + 1)] / [ sqrt(2n - 1)^2 - sqrt(2n + 1)^2 ]
= [ sqrt(2n - 1) - sqrt(2n + 1) ] / [ 2n - 1 - (2n + 1) ]
= [ sqrt(2n - 1) - sqrt(2n + 1) ] / (-2)
= (1/2) [ sqrt(2n + 1) - sqrt(2n - 1) ]

So actually it collapses very nicely. Rewriting each of the terms, you have
(1/2) [ sqrt(3) - sqrt(1) ] + (1/2) [sqrt(5) - sqrt(3) ] + (1/2) [ sqrt(7) - sqrt(5) ] + ... + (1/2) [sqrt(2n + 1) - sqrt(2n - 1)]

And you can see the sqrt(3) terms in the first one cancels the -sqrt(3) in the second, the sqrt(5) terms cancel, and so forth, leaving

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

 

=180600

Answer 1

Yes, it does make sense. If you look at 

(1/1+√3)+(1/√3+√5)+(1/√5+√7)+...+ (1/(√(2n-1)) + (√(2n+1)) = 300

as an equation, then the question would be for which n the sum is equal to 300.

Other than this all calculations look accurate.