An Introduction to Mathematics: For Students of Economics by J. Parry Lewis (auth.)

By J. Parry Lewis (auth.)

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41/2 2 40=15°=( -3) 0 =1 (c) Ratios a x If b y then a a+x b b+y a-x b-y ma+nx mb+ny ma-nx mb-=ny 32a -5x 32b - 5y ' etc. m and n being any real quantities CHAPTER II THE SUMMATION AND CONVERGENCE OF SOME SIMPLE SERIES So he matured by a progression The Lady's Not for Burning CHRISTOPHER FRY: 1. The arithmetic progression One of the most common examples of an Arithmetic Progression is afforded by a salary scale in which there is a constant increment. This constant increment is, in fact, the distinguishing feature of an Arithmetic Progression, which is defined as follows : Definition : A series of quantities taken in order form an Arithmetic Progression if they increase or decrease by a constant amount, which is called the common difference.

In 1966 the tax rose to £0·63 per record, and so in order still to spend exactly £42 on them I bought only n -15. How many records did I buy in 1964, and at what price1 EXERCISE 32 ALGEBRA (b) Simultaneous equations in two unknowns, one equation being linear and the other quadratic : Suppose that we have the following information. Two pictures are to be framed. One is square and the other is twice as long as it is broad. Framing them requires 14 feet of wood and 6 square feet of glass. We want to find the size of each picture.

Example: I am entitled to an annual income of £1,000 now and in each of the next nine years. Because the promise of money in the future is less useful to me than having that sum of money now, I would be prepared to exchange the promise of £1,000 next year for £900 now. I would also be prepared to exchange the promise of £1,000 in the following year for £810 now. And so on. For how much would I sell my complete entitlement? How different would my selling price be if the annuity lasted for (a) 20 years?

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