Question

When evaluating the sum of a series 5∑i=1 (-5xi+8) and x1 through x5 are given; why does i=1 remain the same and not elevate 1 through 5?

Answer 1

\[\sum_{i=1}^5 x_i=x_1+x_2+x_3+x_4+x_5\]

Answer 2

not sure what "elevate" means in this context, but if you know the \(x_i\) then this says add them

Answer 3

But why does i=1 always remain the same?

Answer 4

it doesn't
it goes from 1 to 5

Answer 5

\[\sum_{i=1}^na_n=a_1+a_2+a_3+...+a_n\]

Answer 6

if you are asking why you always start at \(i=1\) you don't
you could start at say \(i=10\) if you like

Answer 7

i think maybe it is confusing because sometimes you see an \(i\) in the formula, like \(\sum_{i=1}^5 i^2=1^2+2^2+3^2+4^2+5^2\) but whatever \(a_i\) is you are adding the terms

Answer 8

For example 4∑j=1 (-1)^j j j=1 was elevated 1 to 4 to find the separate pieces for the sum.

Answer 9

and so if you know \(x_1=3,x_2=8,x_3=5,x_4=9\) then
\(\sum_{i=1}^4=3+8+5+9\)

Answer 10

you mean it was in the exponent?
it might be in the exponent, it might not

Answer 11

for example in
\[\sum_{i=1}^52^i\] it is
you would get \(2+4+8+16+32\)
but in
\[\sum_{i=1}^5(2i-1)\] it is not
you would get \[1+3+5+7+9\]

Answer 12

you could have an \(i\) in the exponent, or on the ground floor, or you could know for some other reason what all the terms are. you do not necessarily have a formula, although usually you do