Скачать или смотреть 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


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