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Examine the sequence 1 + 1/3 + (1/3)^2 + … + (1/3)^n Under what condition does it converge? What does it converge to?

This is a sequence in the form 1 + c + c² + … cⁿ

1 + c + c² + … cⁿ * (1 - c) = 1 – cⁿ⁺¹

So we can rewrite the sequence as

1 – c...

Answered by Hanaan Y. • Maths tutor

3001 Views

Consider a differential equation where dx/dt = -axt. Find an equation for x(t).

Starting from dx/dt = -axt. We treat dx and dt as infinitessimal factors of x and t, therefore fundemental mathematical operations still apply. Rearranging the equation to g...

Answered by Cal L. • Maths tutor

4626 Views

How do you expand brackets? eg. (2x+3)(3x+4)

Use the FOIL method for: (2x+3)(3x+4)

First e.g. multiply first two numbers (2x and 3x)

Outside e.g. 2x and 4

Answered by Naba C. • Maths tutor

5378 Views

How do you differentiate a function comprised of two functions multiplied together?

The product rule is useful when you’re dealing with a function comprised of two functions multiplied together. Generally, if you have a function of the form y = f(x)g(x), then the derivative of the functi...

Answered by Elliot G. • Maths tutor

9153 Views

Solve this simultaneous equation: 5x+6y=3 and 2x-3y=12.

Firstly, I will provide a mark scheme and then a full explanation underneath. 5x+6y=3. (1) 2x-3y=12. (2). (5x+6y=3)+(2(2x-3y=12)). (5x+6y=12)+ (4x-6y=24). 9x=27. x=3. Put x is (1) 5(3)+6y=3=15+6y=3. 6y=-1...

Answered by Ashni M. • Maths tutor

12200 Views