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JEE Advanced Sequences and Series questions with solutions

AP, GP, HP and special series. 12 questions from our 2016–2023 JEE Advanced pattern papers, from the Class 11 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Sequences and Series for JEE Main · Sequences and Series for NDA

JEE Advanced 2023

Let S=Σk=1^10000(1)/(√ k). The greatest integer not exceeding S isJEE Advanced 2023 Paper 2 · hard

JEE Advanced 2021

A sequence is defined by a1=1 and an+1=(an)/(1+n an) for n≥1. The value of Σn=1^101/an isJEE Advanced 2021 Paper 1 · medium

JEE Advanced 2020

Evaluate Σn=1^∞(n^3/((n+1)!).JEE Advanced 2020 Paper 2 · medium

JEE Advanced 2019

Find the value of Σn=1^∞(n^3/((n+2)!). (Use e≈2.71828.)JEE Advanced 2019 Paper 1 · hard
The sum of the infinite series Σn=1^∞(n^2+n+1)/((n+2)!) is ______.JEE Advanced 2019 Paper 2 · medium

JEE Advanced 2018

Evaluate Σn=1^∞(n^2/((n+1)!), giving the answer correct to two decimal places.JEE Advanced 2018 Paper 1 · medium
Find the value of Σk=0^∞(k^2+k+1)/((k+2)!).JEE Advanced 2018 Paper 2 · medium

JEE Advanced 2017

Let S=Σn=1^∞(3n^2+8n+2)/((n+2)!). Find the value of S.JEE Advanced 2017 Paper 1 · medium
Paragraph 2: A sequence (an)n≥1 of positive reals is defined by a1=1 and an+1=(an)/(1+n an) for n≥1. Define bn=1/an. Observe that the recursion turns…JEE Advanced 2017 Paper 2 · 2-question set

JEE Advanced 2016

Define a1=1 and an+1=1/2(an+3/an) for n≥1.JEE Advanced 2016 Paper 1 · medium
Let a,b,c be three distinct positive real numbers in geometric progression such that a, 2b, 3c are in arithmetic progression.JEE Advanced 2016 Paper 2 · medium

Other Mathematics topics

Area Under Curves 13 Binomial Theorem 10 Complex Numbers 24 Conic Sections 34 Differential Equations 18 Differentiation and Application of Derivatives 20 Indefinite and Definite Integrals 18 Limits 19 Matrices and Determinants 28 Permutations and Combinations 18 Probability 38 Quadratic Equations 12 Sets, Relations and Functions 8 Straight Lines and Circles 10 Three Dimensional Geometry 22 Trigonometry and Inverse Trigonometric Functions 18 Vector Algebra 9