1. Prove by telescoping that T(n) = cn*lg(n) + cn under the following condition:

1. Prove by telescoping that T(n) = cn*lg(n) + cn under the following condition:T(n) = c if n = 1T(n) = 2T(n/2) + cn if n > 12. Explain why T(1)s values above 0 versus c will not matter for comparing algorithms. 3. Give an example of a hypothetical situation when you implement a search engine in terms of the search volume and execution time required to complete the search 4. We have two versions of T(n) above depending on whether we use a constant c or not. Explain why the two versions of running time will not make a difference in terms of algorithm analysis using the asymptotic notation.5. For T(n) = cn*lg(n) + cn explain in terms of growth the condition where cn becomes insignificant and therefore ignorable in comparison to cn*lg(n)