Sequences and Series
62 questions across 8 topics.
Sequences and Series of real numbers
- 1Radius of a squared factorial seriesIIT JAM 2026 MSSequences and Series of real numbersMedium
- 11Limsup along even indicesIIT JAM 2026 MSSequences and Series of real numbersHard
- 31Recurrence around the fixed point 2IIT JAM 2026 MSSequences and Series of real numbersMedium
- 1Floor sequence and fractional partIIT JAM 2025 MSSequences and Series of real numbersEasy
- 31A Babylonian recurrence starting negativeIIT JAM 2025 MSSequences and Series of real numbersHard
- 42Radius of n-factorial over n to the nIIT JAM 2025 MSSequences and Series of real numbersEasy
- 1Cauchy property of two sequencesIIT JAM 2024 MSSequences and Series of real numbersEasy
- 41Radius of a shifted power seriesIIT JAM 2024 MSSequences and Series of real numbersEasy
- 24Monotone convergence of recursive sequenceIIT JAM 2023 MSSequences and Series of real numbersMedium
- 25Ratio and root test for seriesIIT JAM 2023 MSSequences and Series of real numbersMedium
- 48Sum of arithmetico-geometric seriesIIT JAM 2023 MSSequences and Series of real numbersMedium
- 1Contractive sequence is CauchyIIT JAM 2022 MSSequences and Series of real numbersEasy
- 31Convergence of reciprocal seriesIIT JAM 2022 MSSequences and Series of real numbersHard
- 41Limit superior and inferior of periodic sequenceIIT JAM 2022 MSSequences and Series of real numbersEasy
- 1Geometric mean limit via Riemann sumIIT JAM 2021 MSSequences and Series of real numbersMedium
- 4Half a binomial rowIIT JAM 2021 MSSequences and Series of real numbersMedium
- 8Absolute convergence and one divergent seriesIIT JAM 2021 MSSequences and Series of real numbersMedium
- 24Two log series coincideIIT JAM 2021 MSSequences and Series of real numbersEasy
- 26Monotone geometric-power recurrenceIIT JAM 2021 MSSequences and Series of real numbersMedium
- 29A ratio condition forcing divergenceIIT JAM 2021 MSSequences and Series of real numbersMedium
- 47A long sum of reciprocal rootsIIT JAM 2021 MSSequences and Series of real numbersMedium
- 54Binomial tail asymptoticsIIT JAM 2021 MSSequences and Series of real numbersHard
- 59Exponential limit with a sine twistIIT JAM 2021 MSSequences and Series of real numbersEasy
- 1Ratio limit implies unboundednessIIT JAM 2020 MSSequences and Series of real numbersEasy
- 11Limit of a two-term average recurrenceIIT JAM 2020 MSSequences and Series of real numbersMedium
- 12Identifying the only convergent seriesIIT JAM 2020 MSSequences and Series of real numbersMedium
- 31Limsup and liminf of a periodic sineIIT JAM 2020 MSSequences and Series of real numbersMedium
- 41Radical limit by dominant powersIIT JAM 2020 MSSequences and Series of real numbersEasy
- 52A Maclaurin coefficient matchingIIT JAM 2020 MSSequences and Series of real numbersMedium
Convergence of sequences
- 1Convergent sequence composed with expIIT JAM 2019 MSConvergence of sequencesEasy
- 12Limit with harmonic sum and exponential rootsIIT JAM 2019 MSConvergence of sequencesMedium
- 41Riemann-sum limit with square rootsIIT JAM 2019 MSConvergence of sequencesMedium
- 51Second-order limit of the defining sequence of eIIT JAM 2019 MSConvergence of sequencesHard
- 2Limit of a power of one plus two over nIIT JAM 2018 MSConvergence of sequencesMedium
- 3Convergence of the maximum and minimum sequencesIIT JAM 2018 MSConvergence of sequencesEasy
- 31Monotone bounded sequence from a harmonic blockIIT JAM 2018 MSConvergence of sequencesMedium
- 3Limit and series of a sequence with exponent tending to zeroIIT JAM 2017 MSConvergence of sequencesMedium
- 32Convergence of the sum of an increasing and a decreasing sequenceIIT JAM 2017 MSConvergence of sequencesMedium
- 48Limit of n times a bounded exponentially damped term plus a sineIIT JAM 2016 MSConvergence of sequencesMedium
- 8Subsequences of a monotone bounded sequenceIIT JAM 2015 MSConvergence of sequencesEasy
- 24Behaviour of the averaged partial sums of the harmonic-root seriesIIT JAM 2014 MSConvergence of sequencesHard
- 2Limit of an expression in a sequence with small ratioIIT JAM 2013 MSConvergence of sequencesMedium
- 18Limit involving a bounded sequence and a sine termIIT JAM 2013 MSConvergence of sequencesMedium
- 4Limit of n times a sum of shifted sine valuesIIT JAM 2012 MSConvergence of sequencesHard
Convergence of series
- 31Series derived from a convergent positive seriesIIT JAM 2019 MSConvergence of seriesHard
- 32Series derived from a convergent positive seriesIIT JAM 2018 MSConvergence of seriesHard
- 24Convergence of two series with exponential decayIIT JAM 2016 MSConvergence of seriesMedium
- 32Sequence and series convergence for a two-branch sequenceIIT JAM 2016 MSConvergence of seriesMedium
- 31Statements that are necessarily false for series of positive termsIIT JAM 2015 MSConvergence of seriesHard
- 9Convergence of a logarithmic series with a parameterIIT JAM 2014 MSConvergence of seriesMedium
- 6Divergence of a series with terms tending to a positive limitIIT JAM 2012 MSConvergence of seriesEasy
Infinite series and its convergence
- 11Telescoping sum of a rational seriesIIT JAM 2019 MSInfinite series and its convergenceMedium
- 41Series with a sum of odd numbers over factorialIIT JAM 2018 MSInfinite series and its convergenceMedium
- 50Telescoping sum of a rational seriesIIT JAM 2017 MSInfinite series and its convergenceMedium
- 54Telescoping series in reciprocals of squaresIIT JAM 2016 MSInfinite series and its convergenceMedium