The Convergence of Darbox Sums and Riemann Sums

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1. Let k >= 1 be an integer, and define Cn = SIGMA (1/(n+i)) as i=1 to kn

(a)Prove that {Cn} converges by showing it is monotonic and bounded.

(b)Evaluate LIMIT (Cn) as n approach to the infinity

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Let be an integer, define .
(a) Prove that converges by showing it is monotonic and bounded
(b) Evaluate
Proof:
(a) Since is a summation of positive number, it is easy ...

Solution Summary

The convergence of Darbox Sums and Riemann Sums are investigated. The expert evaluates a LIMIT to approach the infinity.

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