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Consider the infinite geometric sequence 25 , 5 , 1 , 0.2 , ... (a) Find the common ratio. (b) Find (i) the 10th term; (ii) an expression for the nth term. (c) Find the sum of the infinite sequence.

QUESTION (a) R = U(n+1)/U(n ) = 5/25= 0.2(b) (i) U(10) = 25 x (1/5)^9 = 0.0000128 (ii) U(n) = 25 x (1/5)^(n-1)(c) S = U(1)/(1-r) = 25/(1-(1/5))=25/(4/5))=125/4=31.25

CR
Answered by Carlota R. Maths tutor
5966 Views

Differentiate x^3⋅cos(5⋅x) with respect to x.

In order to solve this problem we will have to use the product rule as follows: d/dx[x^3⋅cos(5⋅x)]=[d/dx(x^3)]⋅cos(5x)+(x^3)⋅[d/dx[cos(5x)]]=(3⋅x^2)⋅cos(5⋅x)+(x^3)⋅−5⋅sin(5⋅x)=3⋅x^2⋅cos(5⋅x)−5⋅x...

TL
Answered by Tianyu L. Maths tutor
5690 Views

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To form the past tense we need to know 3 things: whether we need to use avoir or etre, how to conjugate avoir or etre and the past participle of the verb that we want to be in the past tense.So the first ...

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Answered by Ellie K. French tutor
1491 Views

What are the key things to include in an introduction for an essay?

It is important to lay out your judgement with regard to the question whatever it may be, be concise and clear about where you stand. If there are any key terms or ideas that need explaining, it is a good...

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Answered by Lucy B. History tutor
1957 Views

Describe the attachment study carried out by Lorenz

To test his theory of imprinting in attachment, Lorenz used unhatched goslings to find out whether they will attach to the first moving object they see. He divided a sample of goslings in 2 and let one ha...

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