Page 98 - Excel for Scientists and Engineers: Numerical Methods

CHAPTER 4 NUMBER SERIES 75

Problems

Answers to the following problems are found in the folder "Ch. 04 (Number Series)"
in the "Problems & Solutions" folder on the CD.

1. Evaluate the following infinite series:
(a) 1/2" (b) l/n2 (c) lln!

2. Evaluate the following:

S= 1/1! - 1/2! + 1/3! - 1/4!

3. Evaluate the following infinite series:

Em", where a > 1, x < 1

4. Evaluate the following:
S= 1/2" + 1/3"

5. Evaluate the following:
S = 1/2" - 1/3"

6. Evaluate Wallis' series for 7c:

over the first 100 terms of the series.

7. Evaluate Wallis' series for n, summing over 65,536 terms. Use a worksheet
formula that uses ROW and INDIRECT to create the series of integers.

8. A simple yet surprisingly efficient method to calculate the square root of a
number is variously called Heron's method, Newton's method, or the divide-
and-average method. To find the square root of the number a:
1. Begin with an initial estimate x.
2. Divide the number by the estimate (i.e., evaluate dx), to get a new
estimate
3. Average the original estimate and the new estimate (i.e., (x + dx)/2)
to get a new estimate