Not sure how to interpret nested sums with numbers in between.
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I'm not looking for help with this specific question. I'm just not sure how to deal with nested sums with the numbers between the sigmas. For example, on the first iteration the innermost sum is -16, should that number be multiplied by m, the the middle sum be taken?
sequences-and-series
asked Sep 10 at 20:26
Ismail Majed
82
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up vote
1
down vote
favorite
enter image description here
I'm not looking for help with this specific question. I'm just not sure how to deal with nested sums with the numbers between the sigmas. For example, on the first iteration the innermost sum is -16, should that number be multiplied by m, the the middle sum be taken?
sequences-and-series
asked Sep 10 at 20:26
Ismail Majed
82
Start from left; 1st term is for $k=7$. Thus it will be $7 Sigma_m=6^m=7 m Sigma_n=-2^n=m ldots$ i.e. $7 [ (6 Sigma_n=-2^n=6 ldots) + (7 Sigma_n=-2^n=7 ldots) ]$
– Mauro ALLEGRANZA
Sep 10 at 20:30
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
enter image description here
I'm not looking for help with this specific question. I'm just not sure how to deal with nested sums with the numbers between the sigmas. For example, on the first iteration the innermost sum is -16, should that number be multiplied by m, the the middle sum be taken?
sequences-and-series
asked Sep 10 at 20:26
Ismail Majed
82
enter image description here
I'm not looking for help with this specific question. I'm just not sure how to deal with nested sums with the numbers between the sigmas. For example, on the first iteration the innermost sum is -16, should that number be multiplied by m, the the middle sum be taken?
sequences-and-series
sequences-and-series
asked Sep 10 at 20:26
Ismail Majed
82
asked Sep 10 at 20:26
Ismail Majed
82
asked Sep 10 at 20:26
Ismail Majed
82
asked Sep 10 at 20:26
Ismail Majed
82
asked Sep 10 at 20:26
Ismail Majed
82
82
Start from left; 1st term is for $k=7$. Thus it will be $7 Sigma_m=6^m=7 m Sigma_n=-2^n=m ldots$ i.e. $7 [ (6 Sigma_n=-2^n=6 ldots) + (7 Sigma_n=-2^n=7 ldots) ]$
– Mauro ALLEGRANZA
Sep 10 at 20:30
add a comment |Â
Start from left; 1st term is for $k=7$. Thus it will be $7 Sigma_m=6^m=7 m Sigma_n=-2^n=m ldots$ i.e. $7 [ (6 Sigma_n=-2^n=6 ldots) + (7 Sigma_n=-2^n=7 ldots) ]$
– Mauro ALLEGRANZA
Sep 10 at 20:30
Start from left; 1st term is for $k=7$. Thus it will be $7 Sigma_m=6^m=7 m Sigma_n=-2^n=m ldots$ i.e. $7 [ (6 Sigma_n=-2^n=6 ldots) + (7 Sigma_n=-2^n=7 ldots) ]$
– Mauro ALLEGRANZA
Sep 10 at 20:30
Start from left; 1st term is for $k=7$. Thus it will be $7 Sigma_m=6^m=7 m Sigma_n=-2^n=m ldots$ i.e. $7 [ (6 Sigma_n=-2^n=6 ldots) + (7 Sigma_n=-2^n=7 ldots) ]$
– Mauro ALLEGRANZA
Sep 10 at 20:30
add a comment |Â
1 Answer
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0
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Let's use a simpler example:
$$sum_k=1^2ksum_m=0^k msum_n=-1^m sin(n+m)$$
This breaks down as follows:
$$beginalign* & 1cdot 0cdot big(sin(-1+0)+sin(0+0)big) \ + & 1cdot 1cdot big(sin(-1+1)+sin(0+1)+sin(1+1)big) \ + & 2cdot 0cdot big(sin(-1+0)+sin(0+0)big) \ + & 2cdot 1cdot big(sin(-1+1)+sin(0+1)+sin(1+1)big) \ + & 2cdot 2cdot big(sin(-1+2)+sin(0+2)+sin(1+2)+sin(2+2)big)endalign*$$
answered Sep 10 at 20:38
InterstellarProbe
3,091723
Thank you so much, I get it.
– Ismail Majed
Sep 10 at 20:46
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
Let's use a simpler example:
$$sum_k=1^2ksum_m=0^k msum_n=-1^m sin(n+m)$$
This breaks down as follows:
$$beginalign* & 1cdot 0cdot big(sin(-1+0)+sin(0+0)big) \ + & 1cdot 1cdot big(sin(-1+1)+sin(0+1)+sin(1+1)big) \ + & 2cdot 0cdot big(sin(-1+0)+sin(0+0)big) \ + & 2cdot 1cdot big(sin(-1+1)+sin(0+1)+sin(1+1)big) \ + & 2cdot 2cdot big(sin(-1+2)+sin(0+2)+sin(1+2)+sin(2+2)big)endalign*$$
answered Sep 10 at 20:38
InterstellarProbe
3,091723
Thank you so much, I get it.
– Ismail Majed
Sep 10 at 20:46
add a comment |Â
up vote
0
down vote
accepted
Let's use a simpler example:
$$sum_k=1^2ksum_m=0^k msum_n=-1^m sin(n+m)$$
This breaks down as follows:
$$beginalign* & 1cdot 0cdot big(sin(-1+0)+sin(0+0)big) \ + & 1cdot 1cdot big(sin(-1+1)+sin(0+1)+sin(1+1)big) \ + & 2cdot 0cdot big(sin(-1+0)+sin(0+0)big) \ + & 2cdot 1cdot big(sin(-1+1)+sin(0+1)+sin(1+1)big) \ + & 2cdot 2cdot big(sin(-1+2)+sin(0+2)+sin(1+2)+sin(2+2)big)endalign*$$
answered Sep 10 at 20:38
InterstellarProbe
3,091723
Thank you so much, I get it.
– Ismail Majed
Sep 10 at 20:46
add a comment |Â
up vote
0
down vote
accepted
up vote
0
down vote
accepted
Let's use a simpler example:
$$sum_k=1^2ksum_m=0^k msum_n=-1^m sin(n+m)$$
This breaks down as follows:
$$beginalign* & 1cdot 0cdot big(sin(-1+0)+sin(0+0)big) \ + & 1cdot 1cdot big(sin(-1+1)+sin(0+1)+sin(1+1)big) \ + & 2cdot 0cdot big(sin(-1+0)+sin(0+0)big) \ + & 2cdot 1cdot big(sin(-1+1)+sin(0+1)+sin(1+1)big) \ + & 2cdot 2cdot big(sin(-1+2)+sin(0+2)+sin(1+2)+sin(2+2)big)endalign*$$
answered Sep 10 at 20:38
InterstellarProbe
3,091723
Let's use a simpler example:
$$sum_k=1^2ksum_m=0^k msum_n=-1^m sin(n+m)$$
This breaks down as follows:
$$beginalign* & 1cdot 0cdot big(sin(-1+0)+sin(0+0)big) \ + & 1cdot 1cdot big(sin(-1+1)+sin(0+1)+sin(1+1)big) \ + & 2cdot 0cdot big(sin(-1+0)+sin(0+0)big) \ + & 2cdot 1cdot big(sin(-1+1)+sin(0+1)+sin(1+1)big) \ + & 2cdot 2cdot big(sin(-1+2)+sin(0+2)+sin(1+2)+sin(2+2)big)endalign*$$
answered Sep 10 at 20:38
InterstellarProbe
3,091723
answered Sep 10 at 20:38
InterstellarProbe
3,091723
answered Sep 10 at 20:38
InterstellarProbe
3,091723
answered Sep 10 at 20:38
InterstellarProbe
3,091723
3,091723
Thank you so much, I get it.
– Ismail Majed
Sep 10 at 20:46
add a comment |Â
Thank you so much, I get it.
– Ismail Majed
Sep 10 at 20:46
Thank you so much, I get it.
– Ismail Majed
Sep 10 at 20:46
Thank you so much, I get it.
– Ismail Majed
Sep 10 at 20:46
add a comment |Â
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Start from left; 1st term is for $k=7$. Thus it will be $7 Sigma_m=6^m=7 m Sigma_n=-2^n=m ldots$ i.e. $7 [ (6 Sigma_n=-2^n=6 ldots) + (7 Sigma_n=-2^n=7 ldots) ]$
– Mauro ALLEGRANZA
Sep 10 at 20:30