Question

SUMMATION NOTATION:Getting so annoyed! I was so sure this was the answer. I have tried this problem 3 times, and have 2 attempts left. I was so sure this time :C (comments)

Answer 1

Do you have to do this by hand?

Answer 2

I believe it is 20.

Answer 3

how did you get 23 ? maybe can help you find the error

Answer 4

I did it by hand to be extra sure!

Answer 5

Hartnn, I hand calculated each of the terms up to twenty, then added them. Gave me 23.

Answer 6

so,
2 (-1+ 2-3+4-5+6.....+20)
this right ?

Answer 7

lets take 2 terms at a time
\(2 ( [-1+2]+ [-3+4]+ ... [-19+20])\)
what does each pair equal to ?

Answer 8

I complicated myself by doing a1, a2,a3...uo until 20 then plugging the numbers in the formula xD

Answer 9

thats one way,
but do you get what i am doing ?

Answer 10

not +1 ?

Answer 11

So far, yeah.

Answer 12

and how many such pairs are there ?

Answer 13

FYI, I did what hartnn did so if he gets the same answer go with him.

Answer 14

10 pairs ?

Answer 15

Sorry, my internet is laggy.

Answer 16

no problem

Answer 17

Yes, there would be ten in doing the pairs.

Answer 18

good,
so 1+1+1..1 (10 times)= 10
and 2 (10) = 20
thats your sum!

Answer 19

Damn, all those numbers to figure out how not to do it T-T. Thank you again Hartnn!

Answer 20

Would have been so much easier u__u

Answer 21

lol welcome ^_^
do you also want to know how do we do it using formulas ?

Answer 22

I would o_o

Answer 23

ok, so we have
\(2 [(2+4+6+...20)- (1+3+5+...19)]\)
got this break up ?
we will find the sum of these 2 series separately

Answer 24

these both are arithmetic series
do you know the formula for sum of arithmetic sequences ?

Answer 25

I only know n = a1 + (n – 1)d

Answer 26

thts n'th term formula
what about sum formula ?

Answer 27

this qestion belongs to arithmetic sequence topic, right ?

Answer 28

sn = n(a1+a2) over 2? That is correcto mundo.

Answer 29

its Sn = (n/2) (a1+ an)
an is last term

Answer 30

Oh T-T

Answer 31

so for 1st sequence 2+4+...20
whats a1 = ..
an =..
n= ..
?

Answer 32

a1=2, an=20, n=10?

Answer 33

correct!
so find the sum

Answer 34

I got Sn = 5+n o.o

Answer 35

how ?

Answer 36

and n= 10 as you said

Answer 37

Never mind...should be 15, no?

Answer 38

no

Answer 39

Sn = (10/2) (2+20)
= 5 *22 = ...

Answer 40

Crap, I was using an=10...

Answer 41

5*22=110

Answer 42

yes
so for 2nd sequence 1+3+...19
whats a1 = ..
an =..
n= ..
?

Answer 43

a1=1, an=19, n=9

Answer 44

n= 10
right ?

Answer 45

Wait, I know it isn't 9, but how 10?

Answer 46

1 is 1st term, 19 is last term
(19-1)/2 + 1 = 10

Answer 47

Alright, sorry. Go on.

Answer 48

so find the sum

Answer 49

100

Answer 50

correct!

Answer 51

2 (110-100) = ...

Answer 52

any doubts anywhere ?

Answer 53

No, no doubts Mr Hartnn u__u Thank you very much for your precious time.

Answer 54

you're most welcome ^_^