Calendar: 1877-1878 Page 587

GENERAL LITERATURE AND SCIENCE 585 Express 12345654321 in the scale of 12 and extract its square root in that scale Shew that if Ν be any number the sum of its digits and the radix of tbe scale JV is divisible by If Ρ and c2 d2 then is greater than either ac id or arf be Also if then exceeds by the quantity Sum the series ----9 'erms 2a 2a2 to infinity to η terms id 55 555 to η terms There are four numbers in arithmetical progression if these numbers are increased by 15 respectively the sums are in geometrical progression Find the numbers The squares described on the sides of right-angled triangle are in harmonical progression Compare the lengths of the sides 10 If χ be greater than unity prove that χ χ 11 Find the number of combinations of η things taken together Shew that the number of combinations of η things taken together exceeds the number taken to- gether by unity 12 Write down tbe middle term of 10 also the term involving χ in the expansion of and find the -l