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Prove by induction that, for all integers n >=1 , ∑(from r=1 to n) r(2r−1)(3r−1)=(n/6)(n+1)(9n^2 -n−2). Assume that 9(k+1)^2 -(k+1)-2=9k^2 +17k+6

First, recall how to construct a proof by simple induction in this manner: (1) Assume statement true for n=k, (2) Prove true for n=k+1, (3) Show true for n=1.(1) => ∑(from r=1 to k) r(2r−1)(3r−1)= (k/6...

Answered by Thomas K. • Further Mathematics tutor

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Integrate ((7e^(x/2))/4) with respect to x within the bounds of x=0 and x=2. (Basic introduction to definite integration)

Check to see if anything can be removed from withing the integral and taken out the front. In this case, 7/4 can be taken out the front (as it is not dependent on x), leaving only the term e^(x/2) to be i...

Answered by Niall M. • Maths tutor

3187 Views

¿Qué sabes tú de las relaciones multiculturales en el mundo hispánico?

Puntos que mencionar:-El pueblo indígeno en países como Bolivia (Aymara) y Chile (Mapuche).-España acoge a muchos inmigrantes, por eso su población se Vuelve en muy multicultural. Por ejemplo, muchos vien...

Answered by Benjamin C. • Spanish tutor

4860 Views

Jane Austen uses the character of Mrs. Bennett to provide both humour and social commentary. Discuss.

As the first character to speak in Pride and Prejudice¸ Mrs. Bennett is established as a key character. Austen uses her to introduce the novels main themes of marriage and social status in a comi...

Answered by Tutor169231 D. • English Literature tutor

6949 Views