Question

sigma notation

Answer 1

Evaluate this: \[ \sum_{i=8}^{29}i^2\]

Answer 2

the sum of first n square numbers is equal to :
n(n+1)(2n+1)/6

does this help ?

Answer 3

yes but how about on i = 8 that formula is for i=1

Answer 4

you could figure out the sum from 1 to 29
and figure out the sum from 1 to 7
and subtract the two sums

Answer 5

yes.. so in fact you can subtract two sums ..
can you think about it ?

Answer 6

ok i do like this \[\sum_{i=1}^{22}i^2 \] =22(22+1)(2(22+1)
=(22(23) (2(22+1))/6
=(22(23)(45))/6
=3795

Answer 7

no you calculated the sum of the first 22 numbers

Answer 8

read what phi wrote .. he said what you should do

Answer 9

yes phi i figure it out from 1 -29 but...that i=8 solution....

Answer 10

8415

Answer 11

and figure out 1-7? can u explain pls

Answer 12

yes.. that's good

Answer 13

you want the sum : 8^2+9^2+....+29^2

now if you calculate the sum of 29 first numbers you get
1^2 + 2^2+... + 29^2

but you only need 8 to 29
so you have to subtract the first 7 numbers

Answer 14

you can think like this:
sum(1 to 29) = sum(1 to 7) + sum(8 to 29)

Answer 15

ow i need to subract the 1st 7 number ok nice w8 w8 i do that

Answer 16

how to subract the 1st 7 number i mean where do i put it? sum(1 to 7)= 140

Answer 17

now calculate the first 29 elements sum
and subtract the 1 to 7 from it ..

Answer 18

1 to 7 = 140 8 to 29 = 8415 if i total it 1to 29= 8555
cool i need a shortcut solution

Answer 19

if u subtract it i will get 8415

Answer 20

the shortest thing you can do is figure out
\[ \sum_{i=1}^{29}i^2 = 8555 \]
and then 8555-140= 8415

Answer 21

why are you using 22 and not 29?

Answer 22

no no is that from the other question... if i= 1 i can easyly create a solution

Answer 23

if you are asking about
\[ \sum_{i=8}^{29}i^2 \]
you do it by noticing that
\[ \sum_{i=1}^{7}i^2 + \sum_{i=8}^{29}i^2 = \sum_{i=1}^{29}i^2 \]
and
\[\sum_{i=8}^{29}i^2 = \sum_{i=1}^{29}i^2 - \sum_{i=1}^{7}i^2 \]

Answer 24

u got it! thanks u phi thats the formula my prof i did not write

Answer 25

does the first line make sense?

remember that
\[ \sum_{i=1}^{7}i^2 \]
is short for
\[ 1^2 +2^2 + ...+7^2\]
if we wrote
\[ \sum_{i=1}^{7}i^2 + \sum_{i=8}^{9}i^2 \]
that would be the same as
\[ 1^2 +2^2 + ...+7^2 +8^2 + 9^2\]
or simply
\[ \sum_{i=1}^{9}i^2 \]

Answer 26

yup i got it phi