Infinite Series : Convergence and Divergence (8 Problems)
1)
a) Prove that
N
∑ 1/n(n+1) = 1- (1/N+1)
n=1
Hence, or otherwise, determine whether the following infinite series is convergent or divergent:
b) Determine whether each of these infinite series are convergent or divergent. Justify your answer
∞
i) ∑ n²/n³ +10³
n=1
∞
ii) ∑ 1/tan‾ ¹(n)
n=1
∞
iii) ∑ (-1)ⁿ/In(n)
n=2
2)
a) Express (1/n+1) - (1/n+3) as a single fraction
using this result, or otherwise, prove that
∞
∑ 1/(n² +4n+3) = ½{(3/2)-(1/n+2)-(1/n+3)}
n=0
Hence determine whether the infinite series
∞
∑ 1/(n² +4n+3)
n=0
is convergent or divergent, justify your determination
b) The series
∞
∑ ( n+7)/(4n-1)
n=1
is divergent. Explain in detail why this is the case
https://brainmass.com/math/real-analysis/infinite-series-convergence-and-divergence-8-problems-42068
Solution Summary
The convergence or divergence of series is investigated. The solution is detailed and well presented.