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Series Calculation and Its Convergent Properity

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(a) (i) Fine the sum of the integers from 17 to 92 inclusive.
(ii) Hence find the value of:

92
∑ (5+6i)
i = 17

(b) For each of the sequences below, decide whether it converges, and if it does, state its limit.

(i) a*subscript*n = 7 + 2(0.4)^n / 8(0.3)^n - 8 (n = 1, 2, 3, ... )

(ii) b *subscript* n = 3 - 9n^2 / 5n + 6 (n = 1, 2, 3, ... )

(c) Find the fraction equivalent to the infinite decimal: 0.638 163 816 381

https://brainmass.com/math/real-analysis/series-calculation-convergent-properity-540780

Solution Preview

Question 1

(a)
(i) Find the sum of the integers from 17 to 92 inclusive.

We have (92-17)+1=76 numbers. So the sum is (17+92)*76/2=4142

(ii) Hence find the value of

Using the result in part a, sum is ...

Solution Summary

The solution gives detailed steps on finding the sum of integer series and determining the convergent properties of some certain series. Also, a transformation between infinite decimal and fraction is computed step by step.

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