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What is the sum of the series 2/3 − 2/9 + 2/27 − ....? (PAT Q1 2013)

This is the sum of a geometric series with an infinite number of terms.First, find the common ratio:(-2/9)/(2/3) = -1/3 , (2/27)/(-2/9) = -1/3Therefore, the common ratio is -1/3-1<(-1/3)<1 therefore th...
KM
Answered by Kirill M. • PAT tutor
16423 Views

What is the derivative of ln(x)?

First let y=ln(x). Recall that the exponential function, e x , is defined as the inverse of the logarithmic function, ln(x). To make x the subject of the formula, use the inverse function exp. This gives tha...
BG
Answered by Benjamin G. • Maths tutor
11658 Views

Why is it that sin^2(x) + cos^2(x) = 1?

Let's start with the definition of sin( x ) and cos( x ). We're going to use t rather than x here to avoid confusion, but the idea is exactly the same. Take a unit circle - that is, a circle with centre (0,0...
JT
Answered by John T. • Maths tutor
7443 Views

Prove that 0.565656.... can be expressed as 56/99.

1) Let x=0.565656... 2) Thus 100x=56.565656... 3) Subtracting equation 1) from 2) gives: 99x=56 4) Rearrange for x: x=56/99, Also x=0.565656... from 1) Therefore 0.565656...=56/99
DC
Answered by Daanyaal C. • Maths tutor
4593 Views

How can I move up in my AO2 bands in my History EPQ (AQA)?

Hi there! Your AO2 bands are about how you use evidence in relation to your argument. These are just a few tips about how you can improve. AO2 - 7-10 marks "Evidence of detailed research involving the s...
SD
11894 Views