University:
San Diego State University
Course:
MATH 151 | Calculus II
Academic year:

2023
Views:

208

Pages:

1
Author:

Fachtitelb00

Workshop #20 1. Determine whether the sequence converges or diverges. If it converges, find the limit. √ (−1)n n (a) ln(n + 1) n 5 + 3n (b) n! + 3(5n ) n! (c) (n + 1)! + n2 2n + n3 (d) cos π · n+1 2 2. Consider the sequence 2, 2 21 , 2 13 , 2 14 , 2 51 , . . .. (a) What is the sum of the first three terms? (b) How many terms could you add so that the sum is bigger than 8? (c) How many terms could you add so that the sum is bigger than 20? (d) How many terms could you add so that the sum is bigger than 500? (e) Do you think we can add enough terms so that the sum is as big as we want? Why or why not? 1 1 3. Consider the sequence 12 , 14 , 81 , 16 , 32 , . . .. (a) Compute the following. Sum of the first two terms = Sum of the first three terms = Sum of the first four terms = Sum of the first five terms = Sum of the first six terms = Sum of the first seven terms = (b) Looking at the pattern above, what number does it appear those partial sums are approaching? 4. Suppose there is a sequence a1 , a2 , a3 , a4 , . . ., and each one of the terms is bigger than 13 . (a) How many terms could you add to be sure the sum was bigger than 5? (b) How many terms could you add to be sure the sum was bigger than 27? (c) Do you think we can add enough terms so that the sum is as big as we want? Why or why not?