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(2n+3)²-(2n+1)²=(4n²+12n+9)-(4n²+4n+1)=8n+8= 8(n+1)Hence a multiple of 8

2n+1 will always be an odd number (e.g. if n is equal to 3 the answer would be 7, an odd number) So, we square 2n+1 and write this as (2n+1)² 2n +12n 4n...

U_n+1=1/U_n where U₁= 2/3First of all, we need to find U₂ and U₃ and so on, up until we notice a pattern in the answers. U₂ = 1/(2/3) = 3/2U...

Int() in this case will refer to integralsAnswer is: f(x)=(1-x^2)/(1+x^2)=(2-(1+x^2)/(1+x^2)=-1+2/(1+x^2)=> Int(f(x))=Int(-1+2/(1+x^2))=Int(-1)+2Int(1/(1+x^2))=-x+2tan^-1(x)+C

495/3 = 165 => £165 worth of £1 coins
124 x 0.5 = 62 => £62 worth of 50p coins
We know the number of coins that are NOT 20p coins. Therefore, we can subt...