Question

Hey, could someone help me with a series problem for Calculus II? I'll attach it.

Answer 1

Are you doing Stewart's Calculus book?

Answer 2

Yeah, I thought that I got it correct, but I'm writing my series incorrectly. I don't know how to find the nth term.

Answer 3

What do you think it is?

Answer 4

I thought that it would be \[\sum_{n}^{\infty} 150(1.05^n)\]

Answer 5

Then I googled it and someone said it would be something along the lines of \[\sum_{n}^{\infty} 150(0.05^n+0.05^(n-1)+....)\] but I have no ides how you would write that as a series

Answer 6

After the first day how many mg will be in the body? It says that the day after only 5 percent remains, implying the rest is excavated..

Answer 7

There would be 5% of 150, but then you have to add another 150 for the day, right?

Answer 8

No, only 5% of 150mg because all we care about is what is detected in the body

Answer 9

Now on the second day after 150mg more was taken how much will be detected?

Answer 10

It doesn't say that the previous 5% is going to go away only that 5% will be detected every 150 mg taken so you have a sum of 150*.05 (1) + 150*.05(1) + 150*.05(1)

Answer 11

So 7 mg are detected the first day ? What is the pattern ? How many mg will be detected the nth day?