Calendar: 1873-1874 Page 539

GENERAL LITERATURE AND SCIENCE 539 Solve the equations a- b- -cx χ γ χ Vy j1 45 ץ ζ j2 27 ע zf 29 traveller accomplishes journey of 230 miles in 16 hours by land and water the rates of travelling being as but if the rates were reversed he would save hour 20 minutes on the whole journey Find the distances gone and the rates The sum of the first terms of an arithmetical series is to the sum of the first η terms as m3 is to ns and the sum of terms is zero Prove that η Find the sum of η terms of each of the series of which the terms are 3tf η also the sum to infinity of the series χ x3 2xi 3x &c Prove that -f-y3 is greater than x'ly -j- gy for all real positive values of χ and and find the limits of the value of when נ is less than Establish the law of formation of the successive convergents to continued fraction If when an improper fraction is converted into continued fraction the quotients are au a2 &c an and the last convergent