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CHAPTER VI-MIXED PROBLEMS.
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7, and 7 is the number of terms. If you are acquainted with calculation, then tell me quickly what the sum of the series of fractions in geometrical progrossion here is.
The rule for arriving at the sum of a series in geometrical progression wherein the terms are either inoronsod or decreased (in a specified manper by a given known quantity) :
314. The sum of the series in (pure) geometrical progression (with the given first term, given common ratio, and the given number of terms, is written down in two positions) ; one of these Bums so written down) is divided by the given) first torm. From the resulting) quotient, the given) number of torme is subtracted. The (rosulting) remainder is (then) multiplied by the (given) quantity which is to be added to or to be subtracted (from the terms in the proposed series). The quantity (so arrived at) is (then) divided by the common ratio as diminished by one. The eum of the series in pure geometrical progression written down in) the other (position) has to be diminished by the last) resulting quotient quantity, if the given quantity is to be subtracted (from the terms in the series). If, bowever, it is to be adiled, then the sum of the series in geometrical progression written down in the other position) bas to be increased by tho resulting quotient (already referred to. The result in either caru gives the required gum of the specified series).
Examplex in illustration thereof. 315. The common ratio is 5, the first term is 2, and the quantity to be mulded (to the various termy) iw 3, and the naniber of terms is 4. () you who know the secret of caleulation, think out and tell me quickly the sum of the seriod in geometrical progression, wherein the terms are increased by the specified quantity in the specified manner).
814. Algebraically, +(5-) m + (1 - 1) + o in the sum of the series of the following form : a, arm,(arn)
m).+m and so on.
