Algebraical Exercises and Examination Papers |
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Page 49
... arithmetic means between a and b , and find the sum of the series thus formed . H. A. E. 4 EXERCISE LXIII . 1. Simplify ( 1 ) { 23+ INCLUDING RATIO AND THE PROGRESSIONS . 49.
... arithmetic means between a and b , and find the sum of the series thus formed . H. A. E. 4 EXERCISE LXIII . 1. Simplify ( 1 ) { 23+ INCLUDING RATIO AND THE PROGRESSIONS . 49.
Page 53
... mean proportional between x and y is equal to that between c and d . 8. There are m arithmetic means between 1 and 31 , and the 7th is to the ( m - 1 ) th as 5 to 9 : shew that the number of means is 14 . EXERCISE LXVII . 1. Find the ...
... mean proportional between x and y is equal to that between c and d . 8. There are m arithmetic means between 1 and 31 , and the 7th is to the ( m - 1 ) th as 5 to 9 : shew that the number of means is 14 . EXERCISE LXVII . 1. Find the ...
Page 70
... arithmetic means and four geometric means . 7. If N denote the number of combinations of ʼn things 2 together , prove that the number of combinations of N things 2 together is three times the number of combinations of n + 1 things 4 ...
... arithmetic means and four geometric means . 7. If N denote the number of combinations of ʼn things 2 together , prove that the number of combinations of N things 2 together is three times the number of combinations of n + 1 things 4 ...
Page 100
... mean proportional between a and c , prove that b2 +632 ) ( a2 + b2 + c2 ) . a4 + a2c2 + c4 = b2 ( 22-1 + 233 ) a2 2. Find three numbers in ... arithmetic means between x and y . 2. Sum the following series : ( 1 ) ( 100 EXAMINATION PAPERS .
... mean proportional between a and c , prove that b2 +632 ) ( a2 + b2 + c2 ) . a4 + a2c2 + c4 = b2 ( 22-1 + 233 ) a2 2. Find three numbers in ... arithmetic means between x and y . 2. Sum the following series : ( 1 ) ( 100 EXAMINATION PAPERS .
Page 101
... mean between any two quan- tities is a mean proportional between their arithmetic and har- monic means . 8. The sum of the nth and 2nth terms of a G. P. is k , and the sum of the 2nth and 3nth terms is 7 , find the first term and the ...
... mean between any two quan- tities is a mean proportional between their arithmetic and har- monic means . 8. The sum of the nth and 2nth terms of a G. P. is k , and the sum of the 2nth and 3nth terms is 7 , find the first term and the ...
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Common terms and phrases
7th term a b c d a²+b² arithmetic means arithmetic series Binomial Theorem Cambridge cent common difference continued proportion digits equal equation x²+px+q=0 expansion Extract the square Find the coefficient Find the greatest Find the H. C. F. Find the highest Find the lowest Find the number Find the square Find the sum Find the value following equations following series fraction geometric mean geometrical progression Globe 8vo greatest term half-crowns highest common divisor highest common factor infinity Least Common Multiple lowest common multiple mean proportional Multiply number of combinations PAGES places of decimals Prove the rule quadratic quantities quotient Resolve into factors shew shillings simplest form Solve the equations Solve the following square root Subtract Sum the following Sum the series surd x²+1 x²+2xy
Popular passages
Page 123 - Cn,r or nCr, the number of combinations of n things taken r at a time (without repetitions). The form nCr or even "C, is widely used but the notation Cn,r or C(n,r) or ( J is to be preferred. 6. Roman numeral for "hundred.
Page 130 - Any term may be transposed from one side of an equation to the other provided its sign be changed.
Page 138 - Any factor of an expression is a factor also of any multiple of that expression. Thus, if F represent a factor of an expression A, so that A = nF, then mA = mnF. That is, mA contains the factor F.
Page 77 - A person swimming in a stream which runs 1J miles per hour, finds that it takes him four times as long to swim a mile up the stream as it does to swim the same distance down : at what rate does he swim?
Page 131 - ... divided by the less is 2£ times the quotient of the less by the greater : find them. 3. The difference of two numbers is 15, and half their product is equal to the cube of the less number : find them. 4. The product of two numbers is 24, and their sum multiplied by their difference is 20 : find them. 5. The difference of the squares of two consecutive numbers is 17 : find them. 6. The product of two numbers is 18 times their difference, and the sum of their squares is 117: find them. 7. What...
Page 112 - Find three numbers in geometrical progression such that the sum of the first and last is 20, and the square of the mean 36.
Page 141 - Solve the equations : 1 (2) ax-by = 2a (3) у2+л-у =4, 7. The perimeter of a right-angled triangle is six times as long as the shortest side. What is the ratio of the two sides containing the right angle?
Page 134 - The expression n + \ n (n — 1) b is the sum of n terms of an arithmetical progression, of which the first term is unity and the common difference b. If we make 6 = 0, 1, 2, 3, ... we obtain expressions which are called the general terms of the 2nd, 3rd, 4th, order of polygonal numbers respectively.