Question

Evaluate this series.

Answer 1

@peachpi

Answer 2

That's small enough where you can find each term and add them together.
Plug in 1, 2, 3, 4, 5, and 6 for k then add the results

Answer 3

They should say "expand the series"

Answer 4

expand and evaluate actually

Answer 5

@peachpi what if we calculate by expand the sum? like
\[\sum_{k=1}^6 2k^2 +\sum_{k=1}^6 k-\sum_{k=1}^6 5\] ??

Answer 6

I know you can use the arithmetic series formula for the second one and the third one is 30. I don't know if there's a handy way to do the first sum

Answer 7

we have all formula for them
\[\sum_{k=1}^6 2k^2=2\sum_{k=1}^6 k^2=2\dfrac{6*(6+1)*(2*6+1)}{6}= 210\]

Answer 8

but what I don't know is I can't get 173 which is the right answer if we just "plug in" ha!!

Answer 9

for the middle term, we have \(\dfrac{6(6+1)}{2}=21\)
the last term is just -5
hence 210+21 -5 \(\neq 173\) ha!!

Answer 10

@dan815 what is wrong with my logic???

Answer 11

@peachpi you said the last one is -30?

Answer 12

yes -30 because you're subtracting 5 six times

Answer 13

But if it is -30, we can't get 173 though!! 210+21 -30 = 201

Answer 14

@jim_thompson5910 Hello Mr. Jim, please, help me figure out what is wrong.

Answer 15

I got 182 for the first one

Answer 16

yeah agreed. The sum of the k^2 terms is 91 which doubles to 182

Answer 17

@peachy Thanks a lot. My mistake, :) I calculate 2n+1 = 15, not 13.
@jim_thompson5910 Thanks for quickly respond.

Answer 18

Oh, I got it thank you guys!
I have another question.

Answer 19

The population of blue-green algae in a certain lake is increasing at a rate of 33% per hour. The count was at 5,000 cells per milliliter at noon on August 1. By what date and time will the algae count get to the "high alert" level of 50,000 cells per milliliter? Assume that the algae continues to increase at the same rate.

Answer 20

\[\Large F = P(1+r)^t\]
\[\Large 50,000 = 5,000(1+0.33)^t\]
solve for t

t = number of hours (t = 0 corresponds to noon on Aug 1st)

Answer 21

Oh, I understand it now! Thank you!

Answer 22

no problem