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Proof by induction Base Case when n=1 LHS = 1^3=1 RHS= 1/4(1^2)(1+1)^2=1/4(1)(2^2)=1/4(4) Assume true for n=k so ∑r^3= 1/4k^2(k+1)^2 For n=k+1 ∑r^3 = ∑k terms + (k+1)^3 = 1/4(k^2)(k+1)^2 + (k+1)^3 = 1/4(k^2)...

sin^2(x) + sin(x) + cos^2(x) + cos(x) = cos(x)sin(x) + cos(x) + sin(x) +1 (sin^2(x) + cos^2(x) =1) Therefore; 1 +sin(x) + cos(x) = cos(x)sin(x) + sin(x) +cos(x) +1 Cancelling out on both sides cos(x)sin(x) =...

Whilst the US Constitution makes no reference to which is more important than the other, the Senate can be seen as more important for a number of reasons. Senators are elected every six years, as opposed to ...

List Trigonmetric identities which could help to simpilfy integral Use cos(2x)= Cos 2 x-sin 2 x and sin 2 x=1-cos 2 x Sub identity 2 into 1 and rearrange to show Cos 2 x=(1+cos2x)/2 and integrate to find the...

First of all, practising oral questions does not mean no writing. The first task to do is to copy down the question, look for key words and confirm what is being asked. Lot of students answer the wrong quest...