Calendar: 1880-1881 Page 637

general literature and science 637 Define recurring series Shew that the series is recurring series and hence find its sum to η terms 10 Prove that &2 c2 a2 unless 11 The product of any η successive integers is divisible by If number consists of η digits its cube will consist of not less than 371-2 digits nor more tha If η be prime number shew that η -f- is divisible by 12 What are the odds against throwing twice at least in three throws with two dice 13 Shew that if be rational and integral equa- tion and be root of it is divisible by χ Find the remainder when is not root of and hence find the value of φ α φφ &c when γ are roots and φ χ is rational integral function of 14 In an equation imaginary roots occur in pairs Solve the equation 343 21 of which and- -- are roots 15 Assuming that every equation has root hence shew that every equation of the nth degree has η roots and no more What is meant by an equation of the nth degree 16 Express am -Λ terms of being positive integer