Alternating Series: -1/3 + 2/4 - 3/5 + 4/6 - 5/7 + ...
- Thread starter summergrl
- Start date
Check the two conditions of the alternating series.
Your series: \(\displaystyle \L\\\displaystyle\sum_{n=1}^{\infty}(-1)^{n}\frac{n}{n+2}\)
Is it true that: \(\displaystyle \L\\a_{1} \;\ > \;\ a_{2} \;\ > \;\ a_{3} \;\ > \;\ .... \;\ > \;\ a_{k} \;\ > \;\ ....\)
Check the limit:
\(\displaystyle \L\\\lim_{k\to\infty}\frac{n}{n+2}\). Does it equal 0?.
Your series: \(\displaystyle \L\\\displaystyle\sum_{n=1}^{\infty}(-1)^{n}\frac{n}{n+2}\)
Is it true that: \(\displaystyle \L\\a_{1} \;\ > \;\ a_{2} \;\ > \;\ a_{3} \;\ > \;\ .... \;\ > \;\ a_{k} \;\ > \;\ ....\)
Check the limit:
\(\displaystyle \L\\\lim_{k\to\infty}\frac{n}{n+2}\). Does it equal 0?.
