Calendar: 1886-1887 Page 678

680 GENERAL LITERATURE AND SCIENCE fraudulent tradesman sells piece of cloth for 31 yards at 19s 6d yard what was his profit from having used yard measure which was one inch too short man bought £500 three per cent stock when consols were at 93J after receiving one dividend he sold at 96f What did he gain by the transaction Solve the equations 56 Γ-3 xyz ן48 yz xy ζ If be the first term and the common difference of an arithmetical progression find the formula for the sum of η terms If series of numbers be such that each is half the sum of the two others which stand before and after it prove that they form an Prove that the arithmetic geometric and harmonic means between two numbers form geometric progression whose common ratio is less than unity If x1 be the between and x3 show that χ is their and also that £ is the between χ and x2 Distinguish accurately between permutations and com- binations If 60 people are waiting for steamboat in which there is only room for 56 in how many different groups may they be taken In how many of these groups w7ill particular man be taken If Si denote the sum of the first η natural numbers and S3 the sum of their cubes prove that S3 Si2 Sum to infinity the series י 32 "י" y3 י 5ע 34 "י" Prove that fal ci c2a2 a2b2