Calendar: 1869-1870 Page 509

GENERAL LITERATURE AND SCIENCE 511 Define recurring series and show how to sum it Find the scale of relation general term and sum of η terms of 288 40 -ן &c Find the quadratic factors of the equation i2 a2 y2 a2 Expand 10g -j- according to the powers of and compute 10ge g1 to the 9th decimal place Divide x'"" by x" and η being whole numbers and write down the last terms of the quotient If the number of combinations of η things taken ρ together be equal to the number taken ρ together find What is the number of permutations taken together in the word absenteeism 10 Divide number into two such parts that the sum of their square roots may be the greatest possible 11 Find two numbers such that the product of their arith- metical geometrical and harmonical means is 64 and their sum is 12 12 Every odd power of is of the form also if η be any number nr is multiple of 42 13 Find the roots of the equations χϊ yi xi i- yi Sx pל x- נ 14 If ax2 bx and α χ bxx have common divisor then axc aCj αΊύ abj bxc ctb IX -Erigononutn Trace the changes in sign and magnitude of sec Θ as θ increases from to 27r and find an expression for all angles which have given secant In any triangle show that cos cos deduce from it cos and tan in terms of the sides