Sia

“working on something—do you want to see a pitch?” Hornik specialized in Internet companies, so he seemed like an ideal investor to Shader. The interest was mutual. Most people who pitch ideas are first-time entrepreneurs, with no track record of success. In contrast, Shader was a blue-chip entrepreneur who had hit the jackpot not once, but twice. In 1999, his first start-up, Accept.com, was acquired by Amazon for $175”
― Adam M. Grant, Give and Take: Why Helping Others Drives Our Success

“A popular feel for scientific endeavors should, if possible, be restored given the needs of the twenty-first century. This does not mean that every literature major should take a watered-down physics course or that a corporate lawyer should stay abreast of quantum mechanics. Rather, it means that an appreciation for the methods of science is a useful asset for a responsible citizenry. What science teaches us, very significantly, is the correlation between factual evidence and general theories, something well illustrated in Einstein’s life. In addition, an appreciation for the glories of science is a joyful trait for a good society. It helps us remain in touch with that childlike capacity for wonder, about such ordinary things as falling apples and elevators, that characterizes Einstein and other great theoretical physicists.”
― Walter Isaacson

“His best-selling book, The Goal, has sold over 6 million copies and has been translated into 35 languages. It continues to be required reading in major business schools.”
― Eliyahu M. Goldratt, The Goal: A Process of Ongoing Improvement

“Notice that if , then and , whereas if
, then and .
(a) If is absolutely convergent, show that both of the
series and are convergent.
(b) If is conditionally convergent, show that both of the
series and are divergent.
44. Prove that if is a conditionally convergent series and
is any real number, then there is a rearrangement of
whose sum is . [Hints: Use the notation of Exercise 43.
an an

0 a
n
an
0
an an
0 an
0
an

an

an

a
n


an

an

a
n


an
r

an
r
Take just enough positive terms so that their sum is greater
than . Then add just enough negative terms so that the
cumulative sum is less than . Continue in this manner and use
Theorem 11.2.6.]
45. Suppose the series is conditionally convergent.
(a) Prove that the series is divergent.
(b) Conditional convergence of is not enough to determine whether is convergent. Show this by giving an
example of a conditionally convergent series such that
converges and an example where diverges.
r an

r

an

n
2
an

an

nan

nan

nan
an

We now have several ways of testing a series for convergence”
― James Stewart, Calculus: Early Transcendentals