sequences: {5, 1, 5, 1, 5, 1,...}; an = (-3)^n / n!

[paulxzt]

1. Find a formula for the general term an of the sequence {5, 1, 5, 1, 5, 1,...}, assuming the pattern continues.

2. Determine whether the sequence {an} converges or diverges. If it converges, find the limit.

an = (-3)^n / n!

can someone help me with these ..
#1 seems easy but i can't seem to get it right..
thanks

 

[stapel]

#1 seems easy but i can't seem to get it right..

Please reply showing what you've tried for (1). For (2), please specify which test you are using to determine convergence or divergence, and show how far you've gotten.

Thank you!

Eliz.

 

[paulxzt]

It just says determine whether it converges or diverges. We started Sequences so if that helps, we didn't get into any other methods yet.

for the sequence {5,1,5,1,5,1...}
am i supposed to apply Fibonacci's sequence?
its starting from a1 = 5 and then subtracting 4.. adding 4.. etc.. how do i write this with the n..

thanks for any help..

 

[pka]

Number 1 is ideal for recursive definition. That is what you have already hinted at.
\(\displaystyle a_1 = 5,\quad n \ge 2\left[ {a_n = a_{n - 1} + 4\left( { - 1} \right)^{n - 1} } \right]\).

Number 2 expects you to apply the ratio test.
\(\displaystyle \L \left| {\frac{{a_{n + 1} }}{{a_n }}} \right|\).