Calendar: 1871-1872 Page 579

the school 579 of afl -px and qx ρ differ by the same quantity ρ -j- If on the extraction of the square root of number figures have been found show that η mure may be found by division Find an algebraical expression which is equal to when η is even and when Λ is odd Give formula for the number of digits in the square root of number of digits Insert η Harmonic means between two given quantities If arithmetical progression show ab ac that ע are in Harmonical progression If tbe th term of an Harmonical progression be and the ntYl term the rth term Find the number of combinations of η things taken together If this number be denoted by prove that η r'm nr- r-2 י י י 'a r- 10 Show how to express given integer in any propjsed scale If in the scale 12 square number ends with single cipher the preceding digit is and the cube of the square root ends with 60 11 Prove the Binomial theorem for positive integral index Show that ----- ζ ז ד The sum of the first coefficients of is L2