Saturday X-tra X-Sheet: 4 Sequences and Series
... The second and fourth term of a converging geometric series are respectively 36 and 16. All the terms are positive. a) Determine the constant ratio b) The first term ...
... The second and fourth term of a converging geometric series are respectively 36 and 16. All the terms are positive. a) Determine the constant ratio b) The first term ...
1 Introduction 2 Sets 3 The Sum Principle
... Consider the set of all arrangements of elements of S. We may break them up into categories by sorting them by their first element. That is, we place them into piles of arrangements, where each pile has all the arrangements with a given object as the first element, and no others. Then by the inducti ...
... Consider the set of all arrangements of elements of S. We may break them up into categories by sorting them by their first element. That is, we place them into piles of arrangements, where each pile has all the arrangements with a given object as the first element, and no others. Then by the inducti ...
ON Prk SEQUENCES + k = b\ a2a3 + k = y2 axa3 + fe ,2 36 [Feb.
... terms a^ (i = 1, 2, 3) of an F-type P3ik sequence which in turn yield two more solutions xi + ^Hi (^ = 2, 3) of (20) such that xt + /Sy^ (i = 1,2, 3) belong to different classes of solutions of (20). Further, it follows by simple induction that, for any integers i,i f s j, the terms CL3i + j and cz3 ...
... terms a^ (i = 1, 2, 3) of an F-type P3ik sequence which in turn yield two more solutions xi + ^Hi (^ = 2, 3) of (20) such that xt + /Sy^ (i = 1,2, 3) belong to different classes of solutions of (20). Further, it follows by simple induction that, for any integers i,i f s j, the terms CL3i + j and cz3 ...
Differences between consecutive numbers of quadruples Take 4
... Problem: Can for every number of steps it should take until the differences are all equal a suitable quadruple of four numbers be found? If yes, prove it, and, if possible, exhibit the quadruple for the given number of steps . If no, for which number of steps can we find no such quadruple? 1st Examp ...
... Problem: Can for every number of steps it should take until the differences are all equal a suitable quadruple of four numbers be found? If yes, prove it, and, if possible, exhibit the quadruple for the given number of steps . If no, for which number of steps can we find no such quadruple? 1st Examp ...
MA131 - Analysis 1 Workbook 2 Sequences I
... 3. Suppose that (an ) and (bn ) are both null sequences, and ε > 0 is given. (a) Must there be an N1 such that |an | < 21 ε when n > N1 ? (b) Must there be an N2 such that |bn | < 12 ε when n > N2 ? (c) Is there an N0 such that when n > N0 both n > N1 and n > N2 ? (d) If n > N0 must |an + bn | < ε? ...
... 3. Suppose that (an ) and (bn ) are both null sequences, and ε > 0 is given. (a) Must there be an N1 such that |an | < 21 ε when n > N1 ? (b) Must there be an N2 such that |bn | < 12 ε when n > N2 ? (c) Is there an N0 such that when n > N0 both n > N1 and n > N2 ? (d) If n > N0 must |an + bn | < ε? ...
Slide 1
... The integers include zero, the positive integers, and the negative integers. The arrows indicate that the numbers go on forever in both directions. ...
... The integers include zero, the positive integers, and the negative integers. The arrows indicate that the numbers go on forever in both directions. ...
