# show series is decreasing

• May 30th 2009, 02:10 AM
diroga
show series is decreasing
Quote:

show $\{ \frac{1}{2n + 1} \}_{n = 1}^{\infty}$ is strictly decreasing.
for a series to be decreasing the next term must be smaller than the current term. $a_n > a_{n +1}$

2n +1 < 2(n +1) + 1 (n^th term and n^th + 1)

2n + 1 < 2n +3

$\frac{1}{2n +1} > \frac{1}{2n + 3}$
the next term is less than the previous therfor the series is decreasing.

Am I correct?
• May 30th 2009, 03:24 AM
pickslides
this sequence (not correct to call it a series, a series infers a summation) is decreasing.

As $n \rightarrow \infty$ , $\frac{1}{2n+1} \rightarrow 0$
• May 30th 2009, 03:41 AM
diroga
Quote:

Originally Posted by pickslides
this sequence (not correct to call it a series, a series infers a summation) is decreasing.

As $n \rightarrow \infty$ , $\frac{1}{2n+1} \rightarrow 0$

I get it, sequence set/list of terms. I know it goes to zero just by looking at the n in the denominator and 1 in the numerator, but I have to show that it is decreasing. That is my question, did i show the sequences is decreasing, satisfactorily?
• May 30th 2009, 03:56 AM
pickslides
Yeppers (Rofl)