#Question 2

Consider the Binomial Theorem. ( x ty ) n = 1=0 xn- jy ' = (0) x " + ( 7 ) x- zy + ...+ (?2 , ) xyn- 1 + ( 12 ) ym 2. Find the coefficient of x7 in the expansion of (1 + x) 11 3. Find the coefficient of xy' in the expansion of (5x2 + 2y3) 6. 4. Solve the recurrence relation together with the initial conditions given. an = an-1 + 6an-2 for n 2 3, a1 = 3, a2 = 6 nsider the necessary and sufficient conditions for the existence of an Euler circuit and path. er Circuit - A connected multigraph with at least two vertices has an Euler circuit if and only if each s vertices has even degree. r Path - A connected multigraph has an Euler path but not an Euler circuit if and only if it has tly two vertices of odd degree. For which values of n do complete graphs Kn have an Euler circuit? For which values of n do complete graphs Kn have an Euler path