extra credit hw viii

2 2 decide whether the innite series obtained by

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ∞ → . 2 (2) Decide whether the infinite series obtained by substituting x=1 the above power series is convergent or divergent. Answer : 2n !! ∞ n n=0 −1 2n − 1 !! = 1 − 2 1 + 4 ·2 3 ·1 − 6 ·4 ·2 5 ·3 ·1 + 8 ·6 ·4 ·2 7 ·5 ·3 ·1 − 10 · 8 · 6 · 4 · 2 9 ·7 ·5 ·3 ·1 + 12 · 10 · 8 · 6 · 4 · 2 11 · 9 · 7 · 5 · 3 · 1 − ··· is convergent divergent 3 Check one . into (3) Agree that we may artificially rewrite an infinite series ∞ = an n=0 1 2 as 2a0 +a1 a0 + a1 + a2 + a3 + a4 + a5 + a6 + · · · times a1 +a2 + a2 +a3 + + a3 +a4 + a4 +a5 a5 +a6 + a6 +a7 + +··· Specifically for a0 = 1, a1 =...
View Full Document

Ask a homework question - tutors are online