# Series Calculation and Its Convergent Properity

(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

© BrainMass Inc. brainmass.com October 10, 2019, 6:21 am ad1c9bdddfhttps://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.