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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)(k...
TK
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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 inte...
NM
Answered by Niall M. • Maths tutor
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¿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 vienen ...
BC
Answered by Benjamin C. • Spanish tutor
5261 Views

Why did Mary Queen of Scots arrival in England in 1568 cause problems for Elizabeth?

Background Mary fled into England in May 1568, having been defeated by her Scottish nobles. Following the murder of her dashing but difficult husband Henry Darnley, Mary had responded by marrying the man eve...
KF
Answered by Kimberley F. • History tutor
13485 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 comic manner wit...
TD
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