By J. Parry Lewis (auth.)
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4-1+2+5+ ... ,to20terms 3. The first n even integers, checking your result for simple values ofn. 4. 17 + 13 +9 + ... , to 6 terms, and to 12 terms 5. 80 + 79·5 + 79 + 78·5 + ... , to 160 terms and to 321 terms EXERCISE 42 ALGEBRA 2. The geometric progression As Malthus pointed out, a population tends to grow in a geometric progression. If two people beget four children, so that two married couples beget a total of eight children, then (provided the sexes work out nicely and that there are no untimely deaths), there will soon be four new pairs of married couples.
For the first two periods we have the static original situation. In period 3 the level of investment is permanently raised by £0·1m. This adds to incomes in period 3, and so more is available for spending in period 4. ) produces a new national income of £10·19m. Thus even more can be spent in the next month, and to make the consumer goods valued at £9·171m. extra labour is needed, and paid. , which (being higher than before) allows a further increase in spending. And so on ... but for how long?
Other identities are x+2x=3x x 2 -9 =(x +3) (x -3) 28 ALGEBRA There is an important economic parallel. If we divide output ( Y) into two and only two kinds of goods, one called consumer goods (C) other investment goods (I), then, by definition Y=C+l. But if we observe, or suppose, that the output of consumer goods is always a fixed fraction c of total output, then C=cY is true, not by definition, but because of an observed or an assumed pattern of human behaviour. We distinguish between economic identities, such as Y=C+l and economic equations, such as C=cY The former must be true as a matter of definition or pure accountancy.