- #1
Pual Black
- 92
- 1
this is just an arithmetic series but with a small difference. i will show that below
The attempt at a solution
the general arithmetic formula
## S_N=\sum_{n=1}^\infty n##
for my problem
## S_N=\sum_{n=1000}^{2000} n ##
i have to rewrite it so i will just add the even numbers
## S_N=2\sum_{n=500}^{1000} n = 2\frac{n}{2}(first\,term+last\, term) =2 \frac{n}{2}(500+1000)##
now i have a problem
i think (n=number of terms) is 500 but if put this number i will get a wrong answer
if i put n=501 i will the right answer 751500
i have a similar problem
Sum the integers between 1 and 1000 inclusive
a=1
d=1
n=1000
## S_N=\sum_{n=1}^{1000} n =\frac{n}{2}(first\,term+last\, term)= \frac{1000}{2}(1+1000) =500500 ##
so why in problem one i have to put n=501 and in problem two i put n=1000
i think they are just the same but different values
i thought maybe n= last term - first term + 1
is that right?
sorry but i just started studying Infinite Series
The attempt at a solution
the general arithmetic formula
## S_N=\sum_{n=1}^\infty n##
for my problem
## S_N=\sum_{n=1000}^{2000} n ##
i have to rewrite it so i will just add the even numbers
## S_N=2\sum_{n=500}^{1000} n = 2\frac{n}{2}(first\,term+last\, term) =2 \frac{n}{2}(500+1000)##
now i have a problem
i think (n=number of terms) is 500 but if put this number i will get a wrong answer
if i put n=501 i will the right answer 751500
i have a similar problem
Sum the integers between 1 and 1000 inclusive
a=1
d=1
n=1000
## S_N=\sum_{n=1}^{1000} n =\frac{n}{2}(first\,term+last\, term)= \frac{1000}{2}(1+1000) =500500 ##
so why in problem one i have to put n=501 and in problem two i put n=1000
i think they are just the same but different values
i thought maybe n= last term - first term + 1
is that right?
sorry but i just started studying Infinite Series