Finding limit of sum using Riemann Sums

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SUMMARY

The discussion focuses on finding the limit of the sum limn→∞i=1n i/(n2 + i2) by expressing it as a definite integral using Riemann sums. Participants emphasize the importance of understanding Riemann sums as a foundational concept in calculus that connects discrete sums to continuous integrals. The limit can be evaluated by recognizing the function involved and applying the definition of a Riemann sum to transition to the integral form.

PREREQUISITES
  • Understanding of Riemann sums
  • Basic knowledge of limits in calculus
  • Familiarity with definite integrals
  • Concept of convergence in sequences
NEXT STEPS
  • Study the definition and properties of Riemann sums
  • Learn how to evaluate limits involving sums
  • Explore the Fundamental Theorem of Calculus
  • Practice converting discrete sums to definite integrals
USEFUL FOR

Students studying calculus, educators teaching integral calculus, and anyone interested in the application of Riemann sums in mathematical analysis.

hali
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Find the limit limn→∞∑i=1 i/n^2+i^2 by expressing it as a definite integral of an appropriate
function via Riemann sums


...?
 
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Okay, exactly what difficulty are you having? Do you know what a "Riemann sum" is and how it is connected to an integral?
 
Exactly, no idea what it is :/
 

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