Calendar: 1871-1872 Page 518

518 general literature and science When η -f1 digits of square root have been obtained by the common rule show that η more digits may be obtained by division Find by this method the square root of to six places of decimals Prove the binomial theorem for positive integral indices If מ is positive integer and CT the coefficient of x" in the ex- pansion of prove that C0 3C5 Solve the equations bf af Aabx a-b J- 13 25 ga 1086 έ108 10gJ If 5x and 7a find the integral value of χ and prove that 42 c2 c2 62 unless β If -- are successive convergents of continued fraction prove that pnqn pn qn Reduce f$ to continued fraction and apply the result to find the positive integral solutions of 23x- 29j16 If a0 ax e2 -f- be harmonical series and ο rv r2 00 11-1 prove that r" '"2-r where -- is repeated η times and by finding the limit of show that harmonical series is not convergent