5.4.2		Numerical series (convergence tests and summation)

Encouraging Mathematical Inquisitiveness, Carl L. Main, 1:1, 1970, 32-36, 5.2.2
Telescoping Sums and the Summation of Sequences, G. Baley Price, 4:2, 1973,
16-29, 6.3
Calculus by Mistake, Louise S. Grinstein, 5:4, 1974, 49-53, C, 5.1.2, 5.1.4,
5.2.2, 5.2.3, 5.2.5, 5.2.10, 5.6.1, 5.7.2
A Precalculus Unit on Area Under Curves, Samuel Goldberg, 6:4, 1975, 29-35, 0.7
An Interesting Use of Generating Functions, Aron Pinker, 6:4, 1975, 39-45, 0.6,
9.5
A Helpful Device: or One More Use for Pascal's Triangle, Robert Rosenfeld, 8:3,
1977, 188-191, C, 0.9
A Coin Game, Thomas P. Dence, 8:4, 1977, 240-246, 9.9, 9.10
Geometric Series on the Gridiron, Andris Niedra, 9:1, 1978, 18-20
A Note on Infinite Series, Louise S. Grinstein, 9:1, 1978, 46-47, C
A Note on the Integral Test, Peter A. Lindstrom, 9:2, 1978, 105-106, C
Flow Chart for Infinite Series, Thomas W. Shilgalis, 9:3, 1978, 191, C
On Sum-Guessing, Mangho Ahuja, 10:2, 1979, 95-99
The Sum of the Reciprocals of the Primes, W.G.Leavitt, 10:3, 1979, 198-199, C
Calculator-Demonstrated Math Instruction, George McCarty, 11:1, 1980, 42-48,
5.1.1, 5.2.2, 9.6
An Investment Approach to Geometric Series, Robert Donaghey and Warren Gordon,
11:2, 1980, 120-121, C
A Precalculus Approximation of n!, Norman Schaumberger, 11:3, 1980, 202-204, C,
0.2
Summation of Finite SeriesA Unified Approach, Shlomo Libeskind, 12:1, 1981,
41-50, 6.3
Some Sum of Sums, Gerald Lenz, 12:3, 1981, 208-209, C
The Saint Petersburg Paradox and Some Related Series, Allan J. Caesar, 12:5,
1981, 306-308
Infinite Series Flow Chart for the Sum of a(n), Franklin Kemp, 13:3, 1982, 199,
C
Taxes on Taxes, Thomas E. Eisner, 13:4, 1982, 266-269
A Simple Explicit Formula for the Bernoulli Numbers, F. Lee Cook, 13:4, 1982,
273-274, C
The Sums of Zeroes of Polynomial Derivatives, Michael W. Ecker, 13:5, 1982,
328-329, C, 0.7, 5.1.2
Closed-Form Formulas for Quasi-Geometric Series, Arthur C. Segal, 14:2, 1983,
118-122
Sequences, Series and Pascal's Triangle, Lenny K. Jones, 14:3, 1983, 253-256,
C, 6.3
On Sums of Powers of Natural Numbers, Myren Krom, 14:4, 1983, 349-351, C, 9.1
Instant Hindsight!, Norman Schaumberger, 14:4, 1983, 351, C
Evaluating e^x Using Limits, Sheldon P. Gordon, 15:1, 1984, 63-65, 5.3.2
On Problems with Solutions Attainable in More Than One Way, Jean Pedersen and
George Polya, 15:3, 1984, 218-228, 0.2, 0.4
An Almost Correct Series, R.A.Mureika and R.D.Small, 15:4, 1984, 334-338, 9.6
A Monte Carlo Simulation Related to the St. Petersburg Paradox, Allan J.
Caesar, 15:4, 1984, 339-342, 7.2, 9.10
Approximate Angle Trisection, David Gauld, 15:5, 1984, 420-422, 0.6
Inverse Functions, Ralph P. Boas, 16:1, 1985, 42-47, 5.2.1, 5.3.2
On Rearrangements of the Alternating Harmonic Series, Fon Brown and L.O.Cannon
and Joe Elich and David G. Wright, 16:2, 1985, 135-138, C
A Discrete Look at 1 + 2 + ... + n, Loren C. Larson, 16:5, 1985, 369-382, 0.2,
0.9, 3.1, 3.2, 6.3
Cantor's Disappearing Table, Larry E. Knop, 16:5, 1985, 398-399, C
Sums of Rearranged Series, Paul Schaefer, 17:1, 1986, 66-70
How Far Can You Stick Out Your Neck?, Sydney C.K.Chu and Man-Keung Siu, 17:2,
1986, 122-132, 9.6
Counterexamples to a Comparison Test for Alternating Series, J. Richard Morris,
17:2, 1986, 165-166, C
A Case of True Interest, Soo Tang Tan, 17:3, 1986, 247-248, C, 0.8
Another Approach to a Class of Slowly Diverging Series, Norman Schaumberger,
17:5, 1986, 417, C
Computer Algebra Systems in Undergraduate Mathematics, Don Small and John
Hosack and Kenneth Lane, 17:5, 1986, 423-433, 1.2, 5.1.4, 5.1.5, 5.2.2
The Bernoullis and the Harmonic Series, William Dunham, 18:1, 1987, 18-23, 2.2
Pi/4 and ln 2 Recursively, Frank Burk, 18:1, 1987, 51, C, 5.2.5
Behold! Sums of Arctan, Edward M. Harris, 18:2, 1987, 141, C
Generating Functions, William Watkins, 18:3, 1987, 195-211, 6.3, 9.3
Computing Pi, Harley Flanders, 18:3, 1987, 230-235, 5.2.3, 8.1
A Shorter, More Efficient Proof of the limit as n goes to infinity of
[(n!)^(1/n)] / n = 1/e, Joseph Wiener, 18:4, 1987, 319, C
A Simple Proof of Series Convergence, A.R.Amir-Moez, 18:5, 1987, 410, C
Estimating the Sum of Alternating Series, James D. Harper, 19:2, 1988, 149-154
Subharmonic Series, Arthul C. Sogal, 20:3, 1989, 194-200, 9.5
The Power Rule and the Binomial Formula, Stephen H. Friedberg, 20:4, 1989, 322,
C, 5.1.2
Evaluating the Sum of the Series Sum(k^j / M^k), Alan Gorfin, 20:4, 1989,
329-331, C
Sum the Alternating Harmonic Series, Dave P. Kraines and Vivian Y. Kraines and
David A. Smith, 20:5, 1989, 433-435, C, 1.2
Using the Finite Difference Calculus to Sum Powers of Integers, Lee Zia, 22:4,
1991, 294-300, 5.2.1, 5.4.1
The Sum is 1, John H. Mathews, 22:4, 1991, 322, C
Summation by Parts, Gregory Fredricks and Roger B. Nelsen, 23:1, 1992, 39-42,
C, 5.1.2, 5.4.1, 9.3
Summing Geometric Series by Holding a Tournament, Vincent P. Schielack, 23:3,
1992, 210-211, C
Six Ways to Sum a Series, Dan Kalman, 24:5, 1993, 402-421, 9.5
The Series n^m times x^n and a Pascal-like Triangle, David Neal, 25:2, 1994,
99-101
Sum of Squares via the Centroid, Sydney H. Kung, 25:2, 1994, 111, C
Approaches to the Formula for the nth Fibonacci Number, Russell Jay Hendel,
25:2, 1994, 139-142, C, 0.2, 4.5, 9.3, 9.5
FFF #76. Telescoping Series, Eleanor A. Maddock, 25:4, 1994, 309, F
FFF. Pi is approximately ln 4, Frank Burk, 25:4, 1994, 311, F
Sum of Alternating Series (proof by picture), Guanshen Ren, 26:3, 1995, 213, 0.9
Divergence of a Series (by picture), Sidney H. Kung, 26:4, 1995, 301, C
Sums of General Geometric Series (by picture), John Mason, 26:5, 1995, 381, C
FFF #106. The Derivative of the Sum Is the Sum of the Derivatives, Ed Barbeau, 27:4, 1996, 282, F
Bargaining Theory, or Zeno's Used Cars, James C. Kirby, 27:4, 1996, 285-286, C, 6.3
FFF #111. The Bouncing Ball, Daniel J. Scully, 27:5, 1996, 372-373, F
Some Sums of Some Significance, Martha E. Dasef and Steven M. Kautz, 28:1, 1997, 52-55, C
Divergence of the Harmonic Series by Rearrangement, Michael W. Ecker, 28:3, 1997, 209-210, C
Neither a Worst Convergent Series nor a Best Divergent Series Exists, J. Marshall Ash, 28:4, 1997, 296-297, C
Using Simpson's Rule to Approximate Sums of Infinite Series, Rick Kreminski, 28:5, 1997, 368-376
Can You Sum This Familiar Series? (Proof Without Words), Dennis Gittinger, 28:5, 1997, 393, C
Sum of Cubes (proof without words), Alfinio Flores, 29:1, 1998, 61, C
Who Cares if X2 + 1 = 0 Has a Solution?, Viet Ngo and Saleem Watson, 29:2, 1998, 141-144, C, 0.7, 5.2.5, 6.2
FFF #135. Positive Series with a Negative Sum, William A. Simpson, 29:5, 1998, 407, F
A Novel Approach to Geometric Series, Michael W. Ecker, 29:5, 1998, 419-420, C
Harmonic Series, Andrew Cusumano, 30:1, 1999, 34, C
Gabriel’s Wedding Cake, Julian F. Fleron, 30:1, 1999, 35-38, 5.2.10
FFF #141.  Evaluation of a Sum, Joe Howard, 30:2, 1999, 130-131, F
Natural Logarithms via Long Division, Frank Burk, 30:4, 1999, 309-311, C
Things I Have Learned at the AP Reading, Dan Kennedy, 30:5, 1999, 346-355, 0.2, 5.1.1, 5.1.2, 5.2.1, 5.2.6, 6.1
The Series for e via Integration, Marc Chamberland, 30:5, 1999, 397, C