Question

WILL MEDAL! What is the sum of the series?

Answer 1

\[\sum_{n-1}^{20} (5-n)\]

Answer 2

Is this the series?
$$\Large{ \sum_{n=1}^{20} (5-n)}$$

Answer 3

Yes I didn't mean to put the minus sign.

Answer 4

Have you learned arithmatic series?

Answer 5

$$\Large{
\sum_{n=1}^{20} (5-n)
\\\sum_{n=1}^{20} 5-\sum_{n=1}^{20} n

}$$

Answer 6

Yeah I just forgot.

Answer 7

Do you know the formula \[S_n=\frac{n}{2}\{2a+(n-1)d\}\]

Answer 8

I don't remember it.

Answer 9

Ok.... That doesn't matter...

Answer 10

As perl mentioned, \(\sum_{n=1}^{20}5-n=\sum_{n=1}^{20}5-\sum_{n=1}^{20}n\) ok?

Answer 11

Yes

Answer 12

Then what do you think about \[\sum_{n=1}^{20}5\]?

Answer 13

How do I figure it out?

Answer 14

\[\sum_{n=1}^{20}5=5+5+5+\ldots+5(20\ times)\] ok?

Answer 15

So 100?

Answer 16

Bingo!

Answer 17

Then what about \(\sum_{n=1}^{20}n\)?

Answer 18

20?

Answer 19

No No....

Answer 20

Just extend it like I did for \[\sum_{n=1}^{20}5\]

Answer 21

20n?

Answer 22

Like this:
\[\sum_{n=1}^{20}n=1+2+3+\ldots+19+20\]
ok?

Answer 23

Ohhh

Answer 24

210

Answer 25

Then 100-210 right?

Answer 26

-110

Answer 27

yes!!

Answer 28

Thank you so much for your help and not just giving me the answer!!

Answer 29

You're welcome. Cheers!!