may i know how do i show that Sn = n^2 /(n^2 +1) is increasing?

i tried ratio test and it gave an answer of 1..and i cant use comparision test since the denominator is not (n^2 -1).

thanks

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- May 2nd 2010, 08:27 AMalexandrabel90increasing sequence
may i know how do i show that Sn = n^2 /(n^2 +1) is increasing?

i tried ratio test and it gave an answer of 1..and i cant use comparision test since the denominator is not (n^2 -1).

thanks - May 2nd 2010, 08:32 AMMiss
How in earth can you show that the sequence is increasing by the comparison tests or the ratio test ??

Let

Differentiate it and try to remember how to show that the function is increasing by using its derivative ..

If you want to test its convergence (as an infinite series not a sequence), clearly , so .. ? - May 2nd 2010, 09:14 AMalexandrabel90
i learnt in number theory that i can check if a sequence is increasing by whether the following value is greater than or smaller than the previous one.

sorry, i dont really get what you are trying to hint to me:/ - May 2nd 2010, 10:05 AMSoroban
Hello, alexandrabel90!

Quote:

How do i show that: . .is increasing?

Compare to

. . . . . . . . .

. . . . . . .

. .

. . . . . . . . . . . . .

. . For

Therefore: .

- May 2nd 2010, 10:06 AMMiss
is increasing if and only if ..

- May 2nd 2010, 10:43 AMArchie Meade