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workshop10

# workshop10 - ln 2 with maximum allowed error of 10-6 2 If n...

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Workshop 10 1) The series n =1 ( - 1) n +1 n and n =1 1 n 2 n both converge (why?). By coincidence it turns out that their sums are both equal to ln 2. (You’ll understand this coincidence when we study Taylor series.) Which series converges “faster” (and so numerically gives a more eﬃcient way to get a numerical approximation for ln 2)? Justify your answer by computing how many terms of each series must be added up to approximate
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Unformatted text preview: ln 2 with maximum allowed error of 10-6 . 2) If n is suﬃciently large, the following functions of n can be arranged in an increasing order, so that each function is very much larger than the one preceding it. List the functions below in order of size from smallest to largest. n ; n n ; ln n ; 4 n ; 2 n ; n ln n ; 2 ( n 2 ) ; √ n 6 + 1 ; ( n 3 + 1) 2 / 3 . Where would n ! ﬁt in this list? 1...
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