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MATH 1310.03F A Quiz 8 Thursday, November 23, 2000


Student Number:tex2html_wrap_inline84 No.tex2html_wrap_inline86Marks tex2html_wrap_inline88

(25 Marks) Determine convergence or divergence for the series tex2html_wrap_inline90.

Solution. Let tex2html_wrap_inline92. Then tex2html_wrap_inline94 is continuous since tex2html_wrap_inline96 is continuous on tex2html_wrap_inline98 and tex2html_wrap_inline100 for tex2html_wrap_inline102. Also, tex2html_wrap_inline104, so f is decreasing. Moreover,

Hence, tex2html_wrap_inline110 and converges. It follows from the Integral Test that tex2html_wrap_inline90 converges.

Kunquan Lan
Thu Nov 30 12:48:48 EST 2000