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How do I show (2n)! >= 2^n((n!)^2) for every n>=0 by induction?

First we need to be clear how to construct a proof by induction. It has two main parts, the base case and the inductive step . Let P(n) denote that the statement is true for a fixed n. Our base case is to ch...
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Answered by Connor F. • Maths tutor
8355 Views

What is the possessive pronoun in Latin?

The possessive pronoun is translated as 'my' 'your' 'his' 'their' etc in English, and can be easily confused with the personal pronoun in Latin - especially with regards to 'ego, me' etc (the personal pronou...
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Answered by Cian K. • Latin tutor
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Draw an Alkane with the molecular formula C4H8 as well as a possible functional group isomer and state a chemical test you can use to differentiate between the two.

Many organic molecules follow specific formulas to help identify them. For Alkanes this is: C n H 2n+2 (n being the total number of carbon atoms). However, this is not the case with the given molecular formu...
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Answered by Shahaab N. • Chemistry tutor
11475 Views

integrate cos(2x) + sin(3x)

the differential of cos(x) is -sin(x). the differential of cos(2x) is -2sin(2x). you can think of it as differentiating what is in the bracket and putting that in front of the -sin(2x). when differentiating ...
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Answered by Ajay D. • Maths tutor
7882 Views

In November 2017, the Bank of England raised interest rates for the first time in 10 years, increasing the base rate from 0.25% to 0.5%. Please highlight a possible effect of this change on Aggregate Demand in the UK's economy.

One possible effect of this change in interest rate is a decrease in aggregate demand. As interest rates are inversely linked to investment, a component of aggregate demand responsible for approximately 15% ...
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Answered by Josh H. • Economics tutor
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