Hello all,
I just started working with the sum-formula of an arithmetic progression with Sigma.
\(\displaystyle \displaystyle \sum_{k=1}^n\, a_k \, = \, \dfrac{1}{2} \, n \, (a_1 \, + \, a_n)\)
I noticed that this doesn't work for k≠1 and I wasn't taught how to make it, so I formulated this:
If k≠1:
k-h = 1
n1-h = n2
->
\(\displaystyle \displaystyle \sum_{k=h+1}^{n_1} a_k \, = \, \dfrac{1}{2} \, n_2 \,(a_1\, + \,a_{n_1})\)
E.g.:
\(\displaystyle \displaystyle \sum_{k=0}^{14}\, (5k\,+\,3)\,=\,\dfrac{1}{2}\,\times \,15(3\,+\,70)\,=\,570\)
\(\displaystyle \displaystyle \sum_{k=-2}^{22}\, (100k\,+\,10)\,=\,\dfrac{1}{2}\,\times \,25(-190\,+\,2210)\,=\,25250\)
In those examples this worked out. Can I use this as a rule? How come this works this way, that the n1 and n2 are suddenly different values altogether when k≠1?
P.S. I have no idea how to insert math! I used the Tex syntaxes but in Preview the equation won't show up.
I just started working with the sum-formula of an arithmetic progression with Sigma.
\(\displaystyle \displaystyle \sum_{k=1}^n\, a_k \, = \, \dfrac{1}{2} \, n \, (a_1 \, + \, a_n)\)
I noticed that this doesn't work for k≠1 and I wasn't taught how to make it, so I formulated this:
If k≠1:
k-h = 1
n1-h = n2
->
\(\displaystyle \displaystyle \sum_{k=h+1}^{n_1} a_k \, = \, \dfrac{1}{2} \, n_2 \,(a_1\, + \,a_{n_1})\)
E.g.:
\(\displaystyle \displaystyle \sum_{k=0}^{14}\, (5k\,+\,3)\,=\,\dfrac{1}{2}\,\times \,15(3\,+\,70)\,=\,570\)
\(\displaystyle \displaystyle \sum_{k=-2}^{22}\, (100k\,+\,10)\,=\,\dfrac{1}{2}\,\times \,25(-190\,+\,2210)\,=\,25250\)
In those examples this worked out. Can I use this as a rule? How come this works this way, that the n1 and n2 are suddenly different values altogether when k≠1?
P.S. I have no idea how to insert math! I used the Tex syntaxes but in Preview the equation won't show up.
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