Question

Hw11: Problem 10 Previous Problem List Next (1 point) Find all the values of x such that the given series would converge. (100 7n The series is convergent from x- tox= , left end included (YN): right end included(Y,N):

Answer 1

(10r)" 7t

$\tiny \mathrm{Series\:Ratio\:Test:}$

an+1 an If there exists an N so that for all n > N, 0 and nlim。1 -L an →00

(10z (n+1 IT dn+1 Cl an 10z n

10z) (n+1) L= lim 10x)n

10n1

= 11021 . lim n→00 (l (n + 1)

$\tiny =\left|10x\right|\cdot \:1$

$\tiny =10\left|x\right|$

The sum converges for L < 1, therefore solve 10| < 1

4 4 10 10

, 10 n 11 COnverges n 11 n=1

For x converges byp . n 11 n1l Series Test:

Therefore, the convergence interval of Σ (10) 'n11- nz1 n

1610 10

, From x =--, left end included Y 10 to z- , Right end included Y Kight end included Y 10