Question

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index summation.

1/3+1/2+3/5+...+5/6

Answer 1

what do you notice about the denominators
1/3, 2/4,3/5,4/6,5/7,6/8,7/9,8/10,9/11,10/12

Answer 2

They increase by 1

Answer 3

\[\frac{1}{3},\frac{2}{4},\frac{3}{5},\frac{4}{6},\frac{5}{7},\frac{6}{8},\frac{7}{9},\frac{8}{10},\frac{9}{11},\frac{10}{12}\]
yeah in the numerators are also being increased by one

Answer 4

10/12=5/6 by the way

Answer 5

and your 1/2 from before equals 2/4

Answer 6

Ohhhhh, okay. THANK YOU!

Answer 7

so the sequence I'm looking at relates to your series

Answer 8

do you know how to come up with summation notation thingy now?

Answer 9

Yes. I was just having a hard time coming up with the equation.

Answer 10

cool stuff!
it was kinda hard to see at first
like I was hmm how is that 5/6 going to come into play
and I notice 1/3 and 3/5 there numerator and denominator each diff by 2
so i multiplied 5/6 by 2/2 and got 10/12 and then seen well this fits everything else now

Answer 11

Oh, I see now. I have another question. What would be the pattern for 2+5/2+3+7/2+...+5/6?

Answer 12

well i see the 5/2 and the 7/2 thingy

Answer 13

*Sorry, the last one is 19/2

Answer 14

those fractions look the most similar out the thingy

Answer 15

so I'm going to see if i can put everything in that form

Answer 16

4/2,5/2,6/2,7/2,...,19/2

Answer 17

4/2 is 2
6/2 is 3

Answer 18

Oh, I see. Thank you. That's all my questions :)

Answer 19

so the bottom is always going to be 2
and the top thingy starts at 4 and ends at 19
there are (19-4+1) numbers
16 numbers I believe

Answer 20

anyways no problem

Answer 21

Oh, how were you able to get the numbers?

Answer 22

\[\sum_{1}^{n?}n/(n+2)\]

Answer 23

you have 4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19
you can count them or do 19-4+1

like pretend you wanted to know how many numbers (inclusive) is between 5 and 12
there are 12-5+1


if you wanted to know how many numbers are between (inclusive) n and k (n>k)
you do n-k+1

Answer 24

Okay, I get it now. Thank you!

Answer 25

well good luck on your setups
let me know if you want me to check something

Answer 26

the sigma signifies the summation. the lower value below the sigma sign signifies from where the value starts, and the upper limit signifies where it ends (I mistakenly wrote it as n, in place of 'i'). The equation n/(n+2) can be seen from the values given, 1/3, 2/4,3/5...

Answer 27

Oh, btw going back to the 1st equation. I tried to plug it in and I got 5/7 for the last part.

Answer 28

for the first question you have 10 numbers

Answer 29

Oh, no. Like the last number for the equation when I tried i/ i +2

Answer 30

\[\sum_{i=1}^{10}\frac{i}{i+2}\]
the last number should give you 10/12

Answer 31

which is 5/6

Answer 32

Oh, nvm. Sorry, my mistake.

Answer 33

you only went to n=5 didn't you? :p

Answer 34

Yeah >_<

Answer 35

knowing the number of numbers is important to figure out what number we should put on top of that sigma thingy

Answer 36

Okay. Thank you! You're a really great help :)

Answer 37

ahhh thanks