Calendar: 1876-1877 Page 591

GENERAL LITERATURE AND SCIENCE 591 P2-P3----P P3-P2 Pi P3 pn-l- pn If be in geometrical progression and 10gc 10g6 logo in arithmetical progression the common difference is If χ be positive and η positive integer Hence prove that the arithmetic mean of Μ quantities is greater than the geometric mean If the coefficient of xr in the expansion of where η is positive integer be represented by φ η prove that φ κ -f- Φ μ φ η φ η Find the sum ot the series 4- י j3 "י Γ fa &ρ where 11 is positive integer Prove that the convergents to continued fraction taken in order are alternately less and greater than tbe continued fraction and that each is nearer tbe true value than the one preceding Find the value of L-L J-1-ן T2 and the first six convergent An event which has happened must have arisen from one of given number of causes required the probability of the existence of any one of these causes 10 purse contains known number of coins but whether any and if so how many are sovereigns is not known coin is drawn and proves to be sovereign Shew that this event doubles the chance of all being sovereign