000RM.dvi
Chapter 30 Sums of powers of natural numbers Notation Sk(n):=1k+2k+···+nk. Theorem 30.1(Bernoulli).Sk(n)is a polynomial innof de ...
808 Sums of powers of natural numbers Exercise 1.Find the sum of the firstnodd numbers. 2.Find the sum of the cubes of the first ...
Chapter 31 A high school mathematics contest Christopher Newport University Regional High School Mathemat- ics Contest, November ...
810 A high school mathematics contest 2.Solve the equation x^2 −|x|−1=0. 3.Let(an)be an arithmetic sequence. Ifap = qandaq = p, ...
811 5.Each day, Hai and Wai separately play a video game and compare scores. Hai’s score on Tuesday was 10% less than his score ...
812 A high school mathematics contest 6.A pointPis given in the interior of a rectangleABCDwithAB= CD=24andAD=BD=5. What is the ...
813 8.In triangleABC,cos(A−B)+sin(A+B)=2. Determine the shape of the triangle. 9.Four small circles of radius 1 are tangent to e ...
814 A high school mathematics contest 10.Two circles of radii 9 and 17 centimeters are enclosed in a rectan- gle with one side o ...
815 11.Find three different prime numbersa,b,cso that their suma+b+c and their productabcboth end in the digit 7. 12.Karen ran a ...
816 A high school mathematics contest ...
Chapter 32 Mathematical entertainments 1 David Wells’ survey of Beauty in Mathematics 2 T. M. Apostol’s mathematical acrostic ...
818 Mathematical entertainments 32.1 Beauty in mathematics: David Wells’ survey^1 Give each of the following theorems a score fo ...
32.1 2 819 LThere is no equilateral triangle whose vertices are plane lattice points. MAt any party, there is a pair of people w ...
820 Mathematical entertainments 32.2 T. M. Apostol’s mathematical acrostic^2 Guess as many WORDS as you can, then write each let ...
32.2 2 821 A Unit of speed 131 9 153 62 B The second cervical vertebra 87 4 177 20 C In opposition 160 2 84 28 145 171 104 D Cou ...
32.2 2 901 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ...
902 Mathematical entertainments ...
Chapter 33 Maxima and minima without calculus 1.We have 1000 feet of fencing and wish to make with it a rectangular pen, at one ...
904 Maxima and minima without calculus 2.A Norman window has a fixed perimetera. Find the largest possi- ble area. r h 2 r 3.A r ...
905 4.A tray is constructed from a square metal sheet by dimensiona× aby cutting squares of the same size from the four corners ...
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