Q1·Section A (Section A)·1 of 60Floor sequence and fractional partLet {an}n≥1\{a_n\}_{n\ge 1}{an}n≥1 and {bn}n≥1\{b_n\}_{n\ge 1}{bn}n≥1 be sequences given by an=[n2n+1]andbn=n2n+1−an.a_n=\left[\frac{n^2}{n+1}\right]\quad\text{and}\quad b_n=\frac{n^2}{n+1}-a_n.an=[n+1n2]andbn=n+1n2−an. Then OptionsA{an}n≥1\{a_n\}_{n\ge 1}{an}n≥1 converges and {bn}n≥1\{b_n\}_{n\ge 1}{bn}n≥1 divergesB{an}n≥1\{a_n\}_{n\ge 1}{an}n≥1 diverges and {bn}n≥1\{b_n\}_{n\ge 1}{bn}n≥1 convergesCBoth {an}n≥1\{a_n\}_{n\ge 1}{an}n≥1 and {bn}n≥1\{b_n\}_{n\ge 1}{bn}n≥1 divergeDBoth {an}n≥1\{a_n\}_{n\ge 1}{an}n≥1 and {bn}n≥1\{b_n\}_{n\ge 1}{bn}n≥1 convergePick an option to check your answer.Show answerShow solution Report a problem with this questionAll questionsQ2 →Keyboard: A–D answer · S solution · ←/→ previous/next