# Thread: show series is decreasing

1. ## show series is decreasing

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

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

2n + 1 < 2n +3

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

Am I correct?

2. this sequence (not correct to call it a series, a series infers a summation) is decreasing.

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

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

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

4. Yeppers