Divergent and Convergent sums

The trees at a national park have been increasing in numbers. There were 200 trees in the first year that the park started tracking them. Since then, there have been one fifth as many new trees each year. Create the sigma notation showing the infinite growth of the trees and find the sum, if possible.

Question

Divergent and Convergent sums

The trees at a national park have been increasing in numbers. There were 200 trees in the first year that the park started tracking them. Since then, there have been one fifth as many new trees each year. Create the sigma notation showing the infinite growth of the trees and find the sum, if possible.

anonymous · Answer

ear

New trees

1

1000

2

200

3

40
 
thats a table

kmeis002 · Answer

Have you studied geometric series, if so, can you find a common ratio and starting value?

anonymous · Answer

i know its divergent and i know the ratio is 1/5 and a sub 1 would be 1,000

anonymous · Answer

$$\sum_{i=1}^{\infty} 1,000(\frac{ 1 }{ 5 }) ^{i-1} $$

im just not sure if the it will be i-1 or just 1

anonymous · Answer

i also know that the sum can't be found

kmeis002 · Answer

Remember;
$$\sum_{n=0}^\infty ar^n $$
converges if 
$$\left | r \right | <1 $$

Your power can start at 0, so index i should start at 0 or 1, its your choice.

Where did the 1000 come from, I see the table but nothing about it in the word problem.

anonymous · Answer

the answer choices are all the same, 1000(1/5) the thing that varies is i-1 and i

kmeis002 · Answer

If your first term is 1000, then the ratio should have a starting power of 0, if the starting term is 200, then the ratio should have a starting power of 1 since 1000*(1/5) = 200

anonymous · Answer

$$\sum_{i=1}^{\infty}1000(\frac{ 1 }{ 5 })^{i-1};1250 trees$$

$$\sum_{i=1}^{\infty}1000(\frac{ 1 }{ 5 }) ^{i-1} ; cant be find$$

$$\sum_{i=1}^{\infty}1000(\frac{ 1 }{ 5 }) ^{i} ; 1250 trees$$

$$\sum_{i=1}^{\infty}1000(\frac{ 1 }{ 5 })^{i} ; cant be find$$

anonymous · Answer

those are ht answer choices

anonymous · Answer

@kmeis002

kmeis002 · Answer

Since it seems to want n = 1 then trees = 1000, then our ratio should be risen to the 0 for its starting term. Therefore, if i starts at 1, r needs to raise to i-1. And the series converges, since r < 1

anonymous · Answer

thank you, i got B wrong, i was confused with the fact that it cant be found, the correct answer was A i believe because it had i-1 and because the sum can be found

anonymous · Answer

The answer is A .. 100% sure , just took the test