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Further Mathematics
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Show that the sum from 1 to n of 1/(2n+1)(2n-1) is equal to n/(2n+1) by Induction

First we check that this is true for n=1: S1 = 1/(1x3)  which is equal to n/(2n+1) for n=1 therefore Sn = n/(2n+1) is true for n = 1. Next assume that it is true for n=k. Sk

JF
13853 Views

Two planes have eqns r.(3i – 4j + 2k) = 5 and r = λ (2i + j + 5k) + μ(i – j – 2k), where λ and μ are scalar parameters. Find the acute angle between the planes, giving your answer to the nearest degree.

Summary of solution: To find the angle between the planes, we must find the normal vector to each plane and then use the scalar product to find the angle between these two normal vectors....

DC
7533 Views

Find the four complex roots of the equation z^4 = 8(3^0.5+i) in the form z = re^(i*theta)

We know that z=re^(itheta) from the definition of the exponential form of a complex number. Hence it follows that: z^4=(re^(itheta))^4=r^4e^(4itheta) We can find z^4 by converting 8(...

GG
5702 Views

Find, without using a calculator, integral of 1/sqrt(15+2x-x^2) dx, between 3 and 5, giving your answer as a multiple of pi

To get the denominator into something usable, you have to complete the square so you have it in one of the forms you can use a trig or hyperbolic substitution for. The minus sign in front of the x2 means ...

LD
4353 Views

Prove by induction that n! > n^2 for all n greater than or equal to 4.

This is a fairly typical example of a question from the Further Maths syllabus.

We wish to demonstrate that for all integers n greater than or equal to 4, n! > n2 .

...

JB
16562 Views

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