0
votes
3answers
105 views

Finding the $n$th term for the sequence $1, \frac{1}{2}, 3, \frac{1}{4}, 5, \frac{1}{6}, \dots$

I have tried using a negative exponent. I need one statement not two, the pattern is $$1, \; \frac{1}{2}, \; 3, \; \frac{1}{4}, \; 5, \; \frac{1}{6}, \dots$$
1
vote
2answers
152 views

Trying to figure out the pattern in this series (2)

I could use some help figuring out what the next row is in the pattern below (and what the rule is generally for each number in the series). I put it in a triangle because I'm pretty sure it has ...
0
votes
2answers
63 views

Need help modifying this binomial expansion

The binomial theorem states that $$(A+B)^n=\sum_{k=1}^{n}{n \choose k}A^{n-k}B^k$$ I need help expressing the following summation as a modified binomial expression: $$\sum_{k=1}^{n}n!{n-1\choose ...