I'm asked to define recursively (definition by induction) [itex]\prod_{k=1}^{n}a_k[/itex](adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Recursive defintion of the product notation

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