Asked by MATH HELP HELPPP

Sn=(n^2+n)^1/2 - n

Prove that Sn < 1/2 for all n
Answered by drwls
Adding 1/4 to the term in parentheses must increase it, for all n. Therefore,

Sn < (n^2 + n + 1/4)^1/2 -n
= (n +1/2) -n = 1/2
Answered by MATH HELP HELPPP
Can you make it a bit longer please its supposed to be 15 marks
Answered by drwls
No. What is a mark, anyway? You should be able to elaborate the proof yourself.
Answered by MATH HELP HELPPP
mark is like grade. Also how is 1/2 < 1/2
Answered by drwls
I never said 1/2 < 1/2.
I started out by saying that, since
Sn = (n^2 + n)^1/2 - n, it must be less than (n^2 + n + 1/4)^1/2 + n.
The reason for that should be obvious.
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