Question Number 223085 by wewji12 last updated on 14/Jul/25
Answered by wewji12 last updated on 14/Jul/25
$$\mathrm{if}\:\mathrm{sequence}\:{A}_{{n}} \:\mathrm{is}\:\mathrm{monotonic}\:\mathrm{decrease}.\: \\ $$$$\bullet\:\:{A}_{{n}} \:\mathrm{satisfie}\:{A}_{\mathrm{0}} \geq{A}_{\mathrm{1}} \geq….\geq{A}_{{n}} \\ $$$$\bullet\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{A}_{{n}} =\mathrm{0} \\ $$$$\mathrm{series}\:\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\left(−\mathrm{1}\right)^{{k}} {A}_{{k}} \:\mathrm{is}\:\mathrm{convergence}… \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{k}} }{{p}_{{k}} }\:\mathrm{conv}..???\:\mathrm{and}\:\mathrm{value}\:\mathrm{is}…?? \\ $$