While this formula is nice for i = 1, it fails when i = -1. It says the sum of -1, 0 and 1 is 1, when it is 0. A formula that works for all values if i is: (n^2 - i^2 + n + i)/2. I derived it from the fact that the sum of a series is equal to the mean times the number of terms. The mean is equal to the first plus the last term over 2 all that time the number of terms, or n + 1. I just thought anyone who came looking for a formula like this left with it.
There's a much easier way to find the sum of an arithmetic series: Sn=n/2(a1+an), in which 'S' is the sum(the value you're trying to find), 'n' is the number of values in the series, 'a1' is the value of the first number in the series(in this case '1'), and 'an' is whatever 'n' is (in this case '100'). With this method, 1+2+...+100 would be S100=100/2(1+100), which equals 5050.
@LoquaciousApe First, thanks for the comment! Your formula is a great addition to the video but there are a few problems with it so let me clarify for everyone else:
S = (n/2)(a1 + an)
S is the sum
n is the number of terms
a1 is the first term
an is the LAST TERM (not necessarily equal to n)
Example: The sum of the first 10 even numbers:
S = (10/2)(2 + 20) <-- Notice that 20 is the 10th even term
Last thing, you need the parenthesis (n/2) because multiplication comes before division.
@LoquaciousApe I appreciate it, this is actually meant to be part of a calculus course in which sigma notation plays a crucial role in summing the area under a curve, but I think this video gets more views from algebra students so the addition of the formula is sure to be useful.
Thank you sir. I am a programmer and I was wondering if you would like me to make a program for your videos to make them much more easily accessible. Students can also do practice problems off the program.
I'm taking Albebra 2 and my teacher gave us an introduction but not the formulas. In my homework, there is a problem where i=1 and it goes up to 5 but it solves for (2i+1). The answer is 35 but I got 31. I was wonder if you could help me?
While this formula is nice for i = 1, it fails when i = -1. It says the sum of -1, 0 and 1 is 1, when it is 0. A formula that works for all values if i is: (n^2 - i^2 + n + i)/2. I derived it from the fact that the sum of a series is equal to the mean times the number of terms. The mean is equal to the first plus the last term over 2 all that time the number of terms, or n + 1. I just thought anyone who came looking for a formula like this left with it.
ROFLmeeWaffle 2 weeks ago
you almost sound like napoleon dynamite!:D
TheMinny11 4 weeks ago
wow!!! my dad gave me a bunch of frormulas to use, but i didn't know how to actally use it. this will help me a lot in mathcounts!
stevenman8 1 month ago
what happens if i != 1?
stoopkitty2 2 months ago
Thank you so much brother for your help, because I just started studying in business admin. so I'm sure gonna come here often!
BettysMusicFly 3 months ago
There's a much easier way to find the sum of an arithmetic series: Sn=n/2(a1+an), in which 'S' is the sum(the value you're trying to find), 'n' is the number of values in the series, 'a1' is the value of the first number in the series(in this case '1'), and 'an' is whatever 'n' is (in this case '100'). With this method, 1+2+...+100 would be S100=100/2(1+100), which equals 5050.
LoquaciousApe 6 months ago
@LoquaciousApe First, thanks for the comment! Your formula is a great addition to the video but there are a few problems with it so let me clarify for everyone else:
S = (n/2)(a1 + an)
S is the sum
n is the number of terms
a1 is the first term
an is the LAST TERM (not necessarily equal to n)
Example: The sum of the first 10 even numbers:
S = (10/2)(2 + 20) <-- Notice that 20 is the 10th even term
Last thing, you need the parenthesis (n/2) because multiplication comes before division.
rootmath 6 months ago
@rootmath Thanks for the corrections. Just thought I'd provide an alternative method for those who might be struggling with using sigma notation
LoquaciousApe 6 months ago
@LoquaciousApe I appreciate it, this is actually meant to be part of a calculus course in which sigma notation plays a crucial role in summing the area under a curve, but I think this video gets more views from algebra students so the addition of the formula is sure to be useful.
rootmath 6 months ago
thank you soooo much!!
xxelaine952xx 7 months ago
Thank you sir. I am a programmer and I was wondering if you would like me to make a program for your videos to make them much more easily accessible. Students can also do practice problems off the program.
TutorialsAndTips101 10 months ago
Thank you for the upload.
I'm taking Albebra 2 and my teacher gave us an introduction but not the formulas. In my homework, there is a problem where i=1 and it goes up to 5 but it solves for (2i+1). The answer is 35 but I got 31. I was wonder if you could help me?
StarLightSylvie 10 months ago
yes.thank youuu
soccerguy130 1 year ago
thanks! nice explanations!
Tanea101 1 year ago