MATH 2B Chapter Notes - Chapter 11.2: Partial Fraction Decomposition, Rational Number, Telescoping Series

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2B
• Professor: George Donaldson

Document Summary

Once we have a sequence of numbers, the next thing to do is to sum them up. Given a sequence (an) n=1 be a sequence: can we give a sensible meaning to the following expression? n=1 an = a1 + a2 + a3 + a4 + . While summing in nitely many terms may seem strange, what isn"t strange is to sum nitely many terms. The nth partial sum of the sequence is the value sn = n i=1 ai = a1 + a2 + + an. We compute the rst few partial sums: s1 = a1 = 4 s3 = a1 + a2 + a3 = What we are constructing is a new sequence (sn) like we have a formula for the nth term of this sequence n=1, the sequence of partial sums. Moreover, the limit of the sequence is lim n sum of the original sequence, and we write sn = 1.