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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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