Question

Please check my answer! write the terms of the series and find the sum.
\[\sum_{k=1}^{4} (k+9)^{2}\]
N =4
534

Answer 1

just expand the series
100, 121....

Answer 2

yes - your answer is correct @marcybaby :)

Answer 3

wait - what you just wote does not agree with what you wrote in the question

Answer 4

woooohooo!! I'm killing myself over here!

Answer 5

how u got that terms?

Answer 6

in your question you wrote an answer of 534 - correct?

Answer 7

but what about the terms?

Answer 8

how did you get that answer?

Answer 9

I'm gonna need a new brain after this!

Answer 10

no need to panic :)

Answer 11

just explain how you got your answer of 534

Answer 12

1/6 (541 N + 57 N^2 + 2 N^3)

Answer 13

where did that expression come from?

Answer 14

HA!!! i have NO idea!

Answer 15

I dont know how the hell I got that answer anymore!

Answer 16

ok, lets take it one step at a time. you are told that the k'th term is equa to \((k+9)^2\).

so, given that, what do you think will be the first first (i.e. when k=1) ?

Answer 17

*first term

Answer 18

i'm so lost now! :(

Answer 19

ok, the sum is given as:\[\sum_{k=1}^{4} (k+9)^{2}\]agreed?

Answer 20

yes

Answer 21

the \(\sum\) symbol means "sum this expression" and the "k=1" at the bottom of this and "4" at its top mean that "k" should take on the values from 1 to 4.

agreed?

Answer 22

yes.

Answer 23

good - this is basically a short hand way of writing the sum.

so, if we expand the sum, we will get:\[\sum_{k=1}^{4} (k+9)^{2}=(1+9)^2+(2+9)^2+(3+9)^2+(4+9)^2\]can you see how that follows?

Answer 24

I do!

Answer 25

gr8! so all you need to do now is work out the numbers on the right and bingo! you should get to your answer. :)

Answer 26

so it shoule be (10)^2? or (1)^2&(9)^2?

Answer 27

you evaluate the expression inside the braces first, e.g.:\[(1+9)^2=(10)^2=100\]

Answer 28

okay!
100, 121, 144, 169

Answer 29

perfect! now just add these up...

Answer 30

534

Answer 31

thats it! great work! :)

Answer 32

see - no new brain required :)

Answer 33

duh! LOL i did that you know. but i thought i had it all wrong

Answer 34

thank you so much!!!! i need a drink!

Answer 35

learn to trust yourself :)

Answer 36

and you're welcome :)

Answer 37

xoxo

Answer 38

go on - you deserve that drink now...

Answer 39

I wish! i have more to do.

Answer 40

hehe - no worries, I'm sure the drinks will still be there when you've finished! :)

Answer 41

Ha! thanks a million! first drink is dedicated to you! :)

Answer 42

cheers to that! :)