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Prove that the square of an odd number is always 1 more than a multiple of 4

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 2 2n+1 2n 1Then multiple out the brackets to give 4n ...
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A sequence is defined as: U(n+1) = 1/U(n) where U(1)=2/3. Find the sum from r=(1-100) for U(r)

U n+1 =1/U n where U 1 = 2/3First of all, we need to find U 2 and U 3 and so on, up until we notice a pattern in the answers. U 2 = 1/(2/3) = 3/2U 3 = 1/(3/2) = 2/3As we can see, U 1 and U 3 are equal, and s...
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Find the indefinite integral of f(x)=(1-x^2)/(1+x^2)

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
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There are 495 coins in a bottle. 1/3 of the coins are £1 coins. 124 of the coins are 50p coins. The rest of the coins are 20p coins. Work out the total value of the 495 coins

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 subtract the number of non-20p coins from the total ...
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Answered by Sim B. • Maths tutor
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25* 3/2

25 3/2 = 25 (3x 1/2) (25 1/2 ) 3 = (square root of 25) 3 (5) 3 = 125
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Answered by Aisha B. • Maths tutor
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