What is the formula for finding the sum of a series of numbers?

For example:





3+19+35+....+307





What formula would i have to use to figure out the answer? Thanks in advance!What is the formula for finding the sum of a series of numbers?
The first step is to find a formula for the terms in the series. In this case it looks like the nth term is 3 + 16*n where n ranges from zero to 19.





Sum from n = 0 to 19 of [3 + 16*n] =





3*20 + 16 * 1/2* 19 * 20 = 3100





Here I used that





Sum from n = 0 to N of 1 equals N + 1





Sum from n = 0 to N of n equals 1/2 N (N+1)What is the formula for finding the sum of a series of numbers?
First answer is correct. To see that it is so, list the first half of the numbers in a column in ascending order, and the second half in an adjacent column in descending order. Note that all of the row sums have the same value. Leonhard Euler figured out this stunt while he was in elementary school.
ah ah too tough..


but just think this way..





3=1squared +2


19= 4 squared +3


and so on..





then u'll get a sum of two series..


so the answer might be in terms of two series, i bet that





or just think of binomial series..
add the first term with the last term, then multiply that by half the number of terms in the sequence, and there's your sum.

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