Sequence and Series: Challenging Problems for JEE Mains and Advanced скачать в хорошем качестве

Sequence and Series: Challenging Problems for JEE Mains and Advanced

In this LIVE session, we are challenging problems for JEE Mains and Advanced challenging problem series Problems Discussed: Problem 1. Each of the terms of an arithmetic series is added to the corresponding terms of a geometric series, forming a new series with first term 3 8 and second term 13 16 . The common difference of the arithmetic series is four times as large as the first term of the geometric series. The common ratio of the geometric series is twice as large as the first term of the arithmetic series. Determine the possible values of the first term of the geometric series. Problem 2. If the sum of 1 + 1 12 1 22 + 1 + 1 22 1 32 + 1 + 1 32 1 42 +···+ is equal to n− 1 n ,n ∈ N, find the value of n. 1 + 1 20252 1 20262 Problem 3. If f(r) = 1+ 1 2 1 3 +··· ..+ 1 r and f(0) = 0, then 10 r=1 (2r +1)f(r) is equal to (A) 11.f(11) − 66 (B) 10.f(11) − 66 (C) 121.f(11) − 66 (D) 121.f(10) − 66. Problem 4.(Multi Option Correct) If a = ∞ r=1 1 2r2−r , b = ∞ r=1 1 (A) a+b =2 (B) b+c =1 (C) a−c =1 (D) None of these Problem 5. 2r2+r , c = ∞ r=1 1 4r3−r then which of the following is (are) correct? For each positive integer n ≥ 1, we define the recursive relation given by an+1 = 1 Suppose that a1 = a2012. Find the sum of the squares of all possible values of a1. 1+an . 1 HWProblems. HW1.(Multi Correct Option) Evaluate the sum ∞ n=1 7n +32 n(n +2) · 3 4 n HW2. Consider a sequence for every positive integer n,a1 = 1 and an+1−3an+2 = 4n.The remainder when a100 is divided by 8 is equal to . HW3.(Multi Correct Option) If g(x) = {x}[x], where {.} and [.] represents fractional part and greatest integer function respectively and f(k) = k+1 Tags: jee challenging questions jee advanced level problems jee mains tough questions hard maths problems for jee jee problem solving series advanced problem solving maths jee high level questions iit jee tough problems concept based jee questions jee mains 2026 January attempt solutions jee mains 2026 paper jee mains 2026 live jee mains 2026 january attempt jee mains 2026 jee 2026 jee mains preparation jee mains maths jee mains physics jee mains chemistry jee aspirants 2026 jee strategy 2026 jee mains tips jee mains motivation jee mains exam jee mains syllabus jee mains important questions jee mains revision jee mains mock test jee mains analysis jee mains expected questions jee mains rank boost