Calendar: 1853-1854 Page 340

33G GENERAL LITERATURE AND SCIENCE Find the least number of ounces of standard gold which can be coined into an exact number of half-sovereigns standard gold being at the rate of 10 176 £3 ji per ounce Solve the equations ץ Γ μ Γ-χ ץ α ץ χ -ν זג -זג If י be the sum of the series formed by taking the 1st and every term of the pth power in an infinite series first term unity the sum of similar series where terms of the ytl1 power are taken then- Pg Qp P- railway train after travelling hour is delayed by an accident for an hour after which it proceeds with $ths of the former speed and arrives at the terminus hours behind time had the accident occurred fifty miles further on the train would have arrived lh 20ra sooner required the length of the line Find three fractions whose denominators are and 18 and sum What is the value of- ץ χ 20 χ -'2ϋ If be the sum of the 4th powers of the first η numbers &c the sums of η terms of geometric series first terms unity and common ratios &c show that- £ &c Μ 10 Find the value of- 1""Η ΊΓ7 &C when is odd 11 Given the sum of three quantities in geometrical progres- sion and the sum of their reciprocals find the sum of the series to infinity 12 If straight line be drawn cutting the sides Β in and and the base Λ Β produced in then Ab Be Ca Ac Β Cb