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The first term of an infinite geometric series is 48. The ratio of the series is 0.6. (a) Find the third term of the series. (b) Find the sum to infinity. (c) The nth term of the series is u_n. Find the value of the sum from n=4 to infinity of u_n.

Note here: u_n indicates u subscript n. (a) u_1 = 48 and the ratio, r = 0.6 Using a calculator, u_2 = 48 x 0.6 = 28.8 u_3 = 28.8 x 0.6 = 17.28 (b) We have the known result that the sum to infinity of a geome...
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Answered by Felix S. • Maths tutor
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Find D when 8x^3-12x^2-2x+D is divided by 2x+1 when the remainder is -2

8x 3 -12x 2 -2x+D...(1) 2x+1...(2) Assume 2x+1=0 so x=-1/2 8x 3 -12x 2 -2x+D=-2... when divided by (2) substitute -1/2 into all X values rearrange to find D
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Answered by Shaun W. • Maths tutor
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How would you differentiate ln(sin(3x))?

To answer this question we require the chain rule, which states that dy/dx=(dy/du)*(du/dx) To use this formula in our question, we can let y=ln(sin(3x))=ln(u) where u=sin(3x) Firstly, using a standard result...
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Answered by Hannah D. • Maths tutor
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Find the shortest distance between the line L: x=1+t, y=1+2t, z=1-t and the point A: (2,3,4)

First, write the line in vector form r =(1 1 1) + t(1 2 -1). Consider a point P on the line such that the line connecting P and A is perpendicular to L. The vector P->A is (2 3 4) - (1 1 1) - t(1 2 -1) = ...
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Answered by Zac T. • Maths tutor
6627 Views

Simplify (3x^2-x-2)/(x^2-1)

This is an algebraic fraction. There is more than one way of solving this expression, but the simplest is to factorise both the top and the bottom quadratic expressions.Firstly we shall simplify the top expr...
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Answered by Venetia L. • Maths tutor
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