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The solution like almost every Methods of Differences questions first involves putting the fraction into partial sums.At this point you would get 3 fractions which can be tricky to deal with. Following wh...

We make use of De Moivre's Theorem which states that (cos(θ)+isin(θ))^n=cos(nθ)+isin(nθ).z^n-1/z^n=cos(nθ)+ isin(nθ)-cos(-nθ)- isin(-nθ)=cos(nθ)+ isin(nθ)-cos(nθ)+ isin(nθ) (by trig relat...

We want to simplify this equation to one that we know how to solve. If we let ((z+1)/z) = w, then we need to solve w^6 = 1, which is more familiar. Now we try to find the modulus and argument of w. w = re...

Use the auxiliary equation k²-5k+6=0. Solving this gives roots k=2 and k=3, which are real and distinct roots. This means that the complementary function is of the form y=Ae^(k₁x)+Be...

Firstly, we note that there are 4 key steps for any proof by induction. (1) Basis : check the statement works for n=1. (2) Assumption : assume the statement is true for n=k. (3) Induction : prove the stat...