- #1
neutrino
- 2,094
- 2
I'm asked to define recursively (definition by induction) [itex]\prod_{k=1}^{n}a_k[/itex]
Well, I wrote down the following:
[tex]\prod_{k=1}^{1}a_k = a_1[/tex]
Assuming [itex]\prod_{k=1}^{n}a_k[/itex] has been defined for some [itex]n\geq1[/itex],
[tex]\prod_{k=1}^{n+1}a_k = a_{n+1}\prod_{k=1}^{n}a_k[/tex]
A similar method was used to define the summation notation in the text, so I used it here.
But the answer given at the back is
[tex]\prod_{k=1}^{0}a_k = 1; \prod_{k=1}^{n+1}a_k = a_{n+1}\prod_{k=1}^{n}a_k[/tex]
I don't understand why the index goes from 1 to 0, and why they have defined it to be 1. Please clarify this.
Well, I wrote down the following:
[tex]\prod_{k=1}^{1}a_k = a_1[/tex]
Assuming [itex]\prod_{k=1}^{n}a_k[/itex] has been defined for some [itex]n\geq1[/itex],
[tex]\prod_{k=1}^{n+1}a_k = a_{n+1}\prod_{k=1}^{n}a_k[/tex]
A similar method was used to define the summation notation in the text, so I used it here.
But the answer given at the back is
[tex]\prod_{k=1}^{0}a_k = 1; \prod_{k=1}^{n+1}a_k = a_{n+1}\prod_{k=1}^{n}a_k[/tex]
I don't understand why the index goes from 1 to 0, and why they have defined it to be 1. Please clarify this.