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Extending the definition of the summation convention

  • Thread starter ppy
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  • #1
ppy
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Homework Statement



let a[itex]_{i}[/itex]=x[itex]^{i}[/itex] and b[itex]_{i}[/itex]=1[itex]\div[/itex] i ! and c[itex]_{i}[/itex]=(-1)[itex]^{i}[/itex] and suppose that i takes all interger values from 0 to ∞. calculate a[itex]_{i}[/itex]b[itex]_{i}[/itex] and calculate a[itex]_{i}[/itex]c[itex]_{i}[/itex]

Homework Equations


i know that in suffix notation a[itex]_{i}[/itex]b[itex]_{i}[/itex] is the same as the dot product as when you have to of the same subscripts you take the sum of a[itex]_{i}[/itex]b[itex]_{i}[/itex] from i=1 to i=3 but i am not really sure
of how to use the part where it says take interger values of i from 0 to ∞ an explanation would be great .
thanks.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
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hi ppy! :smile:
let a[itex]_{i}[/itex]=x[itex]^{i}[/itex] and b[itex]_{i}[/itex]=1[itex]\div[/itex] i ! and c[itex]_{i}[/itex]=(-1)[itex]^{i}[/itex] and suppose that i takes all interger values from 0 to ∞. calculate a[itex]_{i}[/itex]b[itex]_{i}[/itex] and calculate a[itex]_{i}[/itex]c[itex]_{i}[/itex]
it's asking you for ∑ xi/i! and ∑ (-1)ixi :wink:
 
  • #3
329
34
from i=1 to i=3
you actually run i from 1 to ##\infty## not 1 to 3
 

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