By J. Parry Lewis (auth.)
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Extra info for An Introduction to Mathematics: For Students of Economics
S the sum of the ten third parts. The sum of the ten first parts is simply the sum of the first ten squares of the natural numbers ; the sum of the second parts is the sum of the first ten natural numbers, with a minus sign before it ; the ten third parts are all equal to unity and therefore have a sum of ten. More easily we may write this as 10 I; (p2 p=1 10 - p + 1) = I; p2 1 = 10 I; p 1 10 + I; 1 1 n(n+1)(2n+1) n(n+l) 6 2 +n where, in this case, n = 10 giving 10 . 11 . 21- 10 . M. 3 By first expressing the general term in the form given, sum the following series to 8 terms : ExERCISE l.
21- 10 . M. 3 By first expressing the general term in the form given, sum the following series to 8 terms : ExERCISE l. 2,6, 12,20,30, .. 2. l, 6, 15, 28, 45, .. 3. 2, 5, 12, 31, 86, .. general term r(r + l) =r2 +r 2r2 -r r +3r-l 4. Convergency and divergency So far we have always specified a definite number of terms for our series. Sometimes, however, we may think of a series as going on for ever, and so we divide series into finite series and infinite series. Provided we know its general term, a finite series can always be summed, even if we have to resort to writing down all the terms and adding them.
5. 11 1. Let petrol cost £p 1 per gallon and beer £p2 per gallon. One week I buy 4 gallons of petrol and 2 gallons of beer and spend £3 in doing so. The next week I buy 6 gallons of petrol and 6 gallons of beer. I also get fined £50 for failing the breathalyser test, and my total outlay that week is £57·5. What are the unit prices of the two liquids1 2. In 1964 I bought n gramophone records, each at a price of £p, and so spent £42. In 1965 each record bore a tax of £0·35, but by reducing my purchases ton -10 I still spent £42.
An Introduction to Mathematics: For Students of Economics by J. Parry Lewis (auth.)