Calendar: 1880-1881 Page 636

636 GENERAL LITERATURE AND SCIENCE Shew by expanding 10g under two forms that J22 1V to η terms according as מ is even or odd Shew that an infinite series in which all the terms are from and after anv fixed term term to unity Apply this test to the series &c 22 32 42 Find the amount at compound interest of Ρ pounds for η years at given rate per cent the interest being paid times year and shew that the interest thus paid is to the interest of the same at simple interest in the ratio of 2q -f qn 2q nearly where is the interest of one pound for one year Shew that -L -J- -L &c V9a2 12 Prove that one solution of the equation can always be found such that χ and are positive integers and hence find the general solution in positive integers Shew also that the successive values of χ are in an arithmetical pro- gression of which is the common difference and similarly for the values of Find the least solution in positive integers of 355 113y 3888 What is the next smaller solution Eleminate χ between the equations xs -3 ar λ χ י χ8 fa 71