Elements of Finite Differences: Also Solutions to Questions Set for ... the Examinations of the Institute of Actuaries |
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Elements of Finite Differences: Also Solutions to Questions Set for Part 1 ... Joseph Burn,E. H. Brown No preview available - 2008 |
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2nd Paper Algebra Answer approx April.-1st Paper April.-2nd Paper Arithmetic Progression arithmetical mean assume Binomial Theorem cards cent central differences CHAPTER coefficient coin common difference constant Continued Fraction denominator denote the number dice differencing digits drawn Elementary Algebra equal expansion expression find the chance Find the number Find the sum find the value Finite Differences formula gallons Geometric Progression half-crowns harmonic mean Hence inches income indefinite integral integer interpolation Lagrange's Theorem Let x denote logarithm loge miles Multiplying natural numbers nth term obtain Oct.-1st Paper Oct.-2nd Paper order of differences pence places of decimals positive integers problem prove quantities recurring decimal required probability respectively roots Scale of Relation Similarly Sixpences solution Solve the equations square substituting symbols throw total chance total number transposing whence white ball Их
Popular passages
Page 61 - Cn,r or nCr, the number of combinations of n things taken r at a time (without repetitions). The form nCr or even "C, is widely used but the notation Cn,r or C(n,r) or ( J is to be preferred. 6. Roman numeral for "hundred.
Page 53 - Given that the area of a circle varies as the square of its radius...
Page 82 - ... terms of another progression, whose first two terms are 45, 43 ; find the value of n. 2. Find the sum of n terms of a geometrical progression whose first term and common ratio are given. The sum of 2n terms of a geometrical progression, whose first term is a and common ratio r, is equal to the sum of n terms of a progression, whose first term is b and common ratio r2; prove that b must be equal to the sum of the first two terms of the first series.
Page 56 - Gd. in the pound in the second year, his net income after paying income-tax was unaltered. Find his income in each year.
Page 54 - The value of a pound of gold is seventeen times that of a pound of silver, and the weights of equal quantities of gold and silver are in the...
Page 53 - Two vessels contain mixtures of wine and water ; in one there is three times as much wine as water, in the other five times as much water as wine. Find how much must be drawn off from each to fill a third vessel which holds seven gallons, in order that its contents may be half wine and half watec 87.
Page 81 - • 5. Find the sum of n terms of an arithmetic progression, whose first term and common difference are given. Prove that, if n is an odd number, the sum of n terms of the progression is n times the middle term. Find the fifth term and the sum of 5 terms of the progression V2+1, 1, V2~-l ... . 6.
Page 55 - B subscribed £15 more than A. After four months C was admitted, who added £50 to the stock; and at the end of 12 months from C's admission they found they had gained £159; when A withdrawing received for principal and gain £88.
Page 66 - ... if there were 20 shares taken by other subscribers ? 5. What is the chance of throwing 5 with one die ? Also find the chance of throwing with two dice 3, 4, or 12 ; and, lastly, find the chance of throwing with two dice either 7, or else 8, or else 9. 6. There are three events, A, B, C, one of which must happen.