Expressing a Sum in Sigma Notation: 1 + (2/3) + (3/5) + (4/7) + (5/9)

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SUMMARY

The sum 1 + (2/3) + (3/5) + (4/7) + (5/9) can be expressed in sigma notation as Σ(i/(2i-1)) for i ranging from 1 to 5. The numerator follows a linear progression of integers, while the denominator is defined by the formula 2i - 1. This clear pattern allows for a concise representation of the series using sigma notation.

PREREQUISITES
  • Understanding of sigma notation and summation
  • Familiarity with sequences and series
  • Basic algebraic manipulation skills
  • Knowledge of how to identify patterns in numerical sequences
NEXT STEPS
  • Study the properties of sigma notation in mathematical expressions
  • Explore sequences and series, focusing on arithmetic and geometric series
  • Learn about mathematical induction to prove formulas involving sums
  • Investigate more complex series and their convergence
USEFUL FOR

Students studying mathematics, particularly those focusing on algebra and calculus, as well as educators looking for examples of sigma notation in action.

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Homework Statement



"Express the following sum in sigma notation:

1 + (2/3) + (3/5) + (4/7) + (5/9)"

Homework Equations





The Attempt at a Solution



I've figured out what they all have in common (1+2=3, 2+3=5, 3+4=7, 4+5=9) but I've been searching through the book and on the internet how to express this.
 
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Suppose the kth term is n(k)/d(k). Can you find a pattern to how the numerator and denominator change with k?
 
I just figured it out. Apparently I just needed to finally ask for help.

The equation is (i/2i-1) with start i=1 and end at 5.
 

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