Calculus and Analysis: TMA 02 Assignment (Semester 1, University Name)

This document presents a solved assignment for a Calculus and Analysis course, specifically TMA 02. The assignment focuses on several key concepts including Euler's summation formula, logarithmic integrals, and related mathematical analyses. Part (a) involves proving a summation formula using Euler's method. Part (b) deals with a similar summation problem involving a specific function d(n). Part (c) requires the student to work with another function, φ(n), and determine a related expression. Part (d) challenges the student to determine the highest power of 3 that divides 823!. Question 2 involves the definition and analysis of the logarithmic integral li(x) and requires students to derive and apply related formulas. The document provides detailed solutions, making it a valuable resource for students studying Calculus and Analysis.