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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...

KM
Answered by Kirill M. PAT tutor
16397 Views

What is the derivative of ln(x)?

First let y=ln(x).

Recall that the exponential function, ex, is defined as the inverse of the logarithmic function, ln(x).

To make x the subject of the formula, u...

BG
Answered by Benjamin G. Maths tutor
11570 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 rather than x here to avoid confusion, but the idea is exactly the same.

Tak...

JT
Answered by John T. Maths tutor
7354 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...

DC
Answered by Daanyaal C. Maths tutor
4549 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 ...

SD
11821 Views

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