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Maths
A Level

How do you prove the 1^2 +2^2+.....+n^2 = n/6 (n+1) (2n+1) by induction?

There are three simple steps to prove anything by induction.

Step 1: When n=1

12=1

then: 1/6 x 1x (1+1) x (2+1)

=1x2x3/6 =1

Therefore it is true for n=1 

...
VI
Answered by Vaisaalii I. Maths tutor
3965 Views

Express the following as a partial fraction: (4x^2+12x+9) / (x^2+3x+2) .

We first notice that the degree of the numerator is the same as the degree of the denominator so we have an improper fraction which we need to separate into an integer and a proper fraction before we can ...

AP
Answered by Antonia P. Maths tutor
4620 Views

How do I write the function 3cosθ+4sinθ in the form Rsin(θ + α), where R and α are positive constants?

Split it up into steps:

Step 1: Use compound angle trigonometric formula to re-write Rsin(θ + α)

Since generally sin(θ ± φ) = sinθcosφ ± cosθsinφ

Rsin(θ + α) = R(sinθcosα + cos...

OG
Answered by Oliver G. Maths tutor
10878 Views

Calculate the distance of the centre of mass from AB and ALIH of the uniform lamina.

The diagram shows the lamina shape.

To begin, divide the lamina into smaller sections and calculate the area. In this example, the lamina is best divided into sections A, B and C. Calculate the are...

CS
Answered by Chandler S. Maths tutor
4932 Views

Solve x^4+2x^2-3=0

The trick with this question is noticing the hidden quadratic as quartic equations are unsolvable at A-level.

Letting u=x^2 the question becomes u^2+2u-3=0 which most students would be able to solv...

BS
Answered by Ben S. Maths tutor
6795 Views

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