{"@context":"https://schema.org/","@type":"Quiz","name":"

Which of the following series converges?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"NET"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"NET","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/which-of-the-following-series-converges"}],"about":{"@type":"Thing","name":"NET, NUST Entry Test, Mathematics, Sequence and Series, Quiz"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["NET","NUST Entry Test","Mathematics","Sequence and Series","Quiz"],"name":"

Which of the following series converges?

","comment":{"@type":"Comment","text":"We know that for a geometric series if $|r|<1$ then the series converges and if $|r|\\\\geq1$ then the series diverges. The only series with $|r|<1$ is the series $S=1+\\\\frac{1}{2}+\\\\frac{1}{4} + \\\\space...$ with $r=\\\\frac{1}{2}$. Therefore it will converge."},"encodingFormat":"text/markdown","text":"

Which of the following series converges?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"$S=-1-1-1- \\space...$"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"$S=1+1+1+ \\space...$"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"$S=2+4+8+ \\space...$"}],"acceptedAnswer":{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"$S=1+\\frac{1}{2}+\\frac{1}{4} + \\space...$","comment":{"@type":"Comment","text":"We know that for a geometric series if $|r|<1$ then the series converges and if $|r|\\\\geq1$ then the series diverges. The only series with $|r|<1$ is the series $S=1+\\\\frac{1}{2}+\\\\frac{1}{4} + \\\\space...$ with $r=\\\\frac{1}{2}$. Therefore it will converge."},"answerExplanation":{"@type":"Comment","text":"We know that for a geometric series if $|r|<1$ then the series converges and if $|r|\\\\geq1$ then the series diverges. The only series with $|r|<1$ is the series $S=1+\\\\frac{1}{2}+\\\\frac{1}{4} + \\\\space...$ with $r=\\\\frac{1}{2}$. Therefore it will converge."}}},"url":"https://classnotes.xyz/mcqs/which-of-the-following-series-converges"}