## kobeni-chan one year ago Please HELP I've been stuck for an hour ;-; John has taken out a loan for college. He started paying off the loan with a first payment of \$100. Each month he pays, he wants to pay back 1.1 times as the amount he paid the month before. Explain to John how to represent his first 20 payments in sigma notation. Then explain how to find the sum of his first 20 payments, using complete sentences. Explain why this series is convergent or divergent.

1. nincompoop

What have you got so far?

2. kobeni-chan

I don't really know where to start :/

3. nincompoop

That is not a good way to solve the problem, dude

4. is3535

100 100*1.1 100*1.1^2 100*1.1^3 ... 100*1.1^19 There they are. You do the sigma notation.

5. is3535

100 + 100*1.1 + 100*1.1^2 + 100*1.1^3 + ... + 100*1.1^19 = 100(1 + 1.1 + 1.1^2 + 1.1^3 + ... + 1.1^19) = $$100\dfrac{1-1.1^{20}}{1-1.1} = 100\cdot\dfrac{5.7275}{0.1} = 5727.50$$ You must be familiar with Geometric Series. Very helpful skills.

6. is3535

can you took a hour i took a 3 min

7. kobeni-chan

I'm rusty on a lot of material, I'm not looking for ridicule ;-;

8. is3535

100 + 100*1.1 + 100*1.1^2 + 100*1.1^3 + ... + 100*1.1^19 = 100(1 + 1.1 + 1.1^2 + 1.1^3 + ... + 1.1^19) = 1001−1.1201−1.1=100⋅5.72750.1=5727.50 You must be familiar with Geometric Series. Very helpful skills.

9. kobeni-chan

So I just keep raising the exponent?

10. is3535

11. anonymous

theres ur answer 57227.50 fan and medal

12. kobeni-chan

I need help getting to the answer! Thats not the point of OpenStudy

13. anonymous

if ur done close the question

14. kobeni-chan

Please, I don't understand though. I get that you guys might be smarter than me or are jsut eager for medals but I need to be able to explain it.

15. kobeni-chan

@ganeshie8 do you know how to explain this?

16. is3535

IM NOT HERE FOR THE MEDAL IM HERE TO HELP

17. kobeni-chan

@is3535 Ok maybe its just your hulk face or something lol

18. is3535

YEA LOL