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## Sequence and Series

### Mathematics

#### Previous Years Questions

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Let $${a_n} = {({1^2} + {2^2} + .....\,{n^2})^n}$$ and $${b_n} = {n^n}(n!)$$. Then
WB JEE 2022
If a, b, c are in G.P. and log a $$-$$ log 2b, log 2b $$-$$ log 3c, log 3c $$-$$ log a are in A.P., then a, b, c are the...
WB JEE 2022
Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while $$\log \left( {{{5c} \over {2a}}} \right)... WB JEE 2021 The digit in the unit's place of the number 1! + 2! + 3! + .... + 99! is WB JEE 2021 Consider the real valued function h : {0, 1, 2, ...... 100}$$\to$$R such that h(0) = 5, h(100) = 20 and satisfying h(p... WB JEE 2021 Let a, b, c be real numbers, each greater than 1, such that$${2 \over 3}{\log _b}a + {3 \over 5}{\log _c}b + {5 \over 2...
WB JEE 2021
Let I(n) = nn, J(n) = 13.5 ......... (2n $$-$$ 1) for all (n &gt; 1), n $$\in$$ N, then
WB JEE 2020
If a and b are arbitrary positive real numbers, then the least possible value of $${{6a} \over {5b}} + {{10b} \over {3a}... WB JEE 2020 Given that n numbers of arithmetic means are inserted between two sets of numbers a, 2b and 2a, b where a, b$$ \in $$R... WB JEE 2018 In a GP series consisting of positive terms, each term is equal to the sum of next two terms. Then, the common ratio of ... WB JEE 2017 The value of$${2 \over {3!}} + {4 \over {5!}} + {6 \over {7!}} + $$............ is WB JEE 2010 If angles A, B and C are in A.P., then$${{a + c} \over b}$$is equal to WB JEE 2010 The value of n for which$${{{x^{n + 1}} + {y^{n + 1}}} \over {{x^n} + {y^n}}}$$is the geometric mean of x and y is... WB JEE 2010 G.M. and H.M. of two numbers are 10 and 8 respectively. The numbers are WB JEE 2010 Sum of n terms of the following series 13 + 33 + 53 + 73 ......... is WB JEE 2010 If sum of an infinite geometric series is$${4 \over {3}}$$and its 1st term is$${3 \over {4}}$$, then its common ratio... WB JEE 2010 The sum of the infinite series$$1 + {1 \over {2!}} + {{1\,.\,3} \over {4!}} + {{1\,.\,3\,.\,5} \over {6!}} + \,....$$i... WB JEE 2009 The coefficient of xn, where n is any positive integer, in the expansion of (1 + 2x + 3x2 + .......$$\infty$$)1/2 is... WB JEE 2009 For what value of m,$${{{a^{m + 1}} + {b^{m + 1}}} \over {{a^m} + {b^m}}}$$is the arithmetic mean of a and b? WB JEE 2009 If three positive real numbers a, b, c are in A.P. and abc = 4 then the minimum possible value of b is WB JEE 2009 If a, b, c are G.P. (a > 1, b > 1, c > 1), then for any real number x (with x > 0, x$$\ne$$1) logax, logbx, logcx are ... WB JEE 2009 The sum of the infinite series$${\left( {{1 \over 3}} \right)^2} + {1 \over 3}{\left( {{1 \over 3}} \right)^4} + {1 \ov...
WB JEE 2008
If three real numbers a, b, c are in Harmonic Progression, then which of the following is true?
WB JEE 2008
If a, b, c be in Arithmetic progression, then the value of $$(a + 2b - c)(2b + c - a)(a + 2b + c)$$ is
WB JEE 2008
The 5th term of the series $${{10} \over 9},{1 \over 3}\sqrt {{{20} \over 3}} ,{2 \over 3}$$ is
WB JEE 2008
The sum of the series $$(1 + 2) + (1 + 2 + {2^2}) + (1 + 2 + {2^2} + {2^3}) + ....$$ upto n terms is
WB JEE 2008
If the mth term and the nth term of an A.P. are respectively $${1 \over n}$$ and $${1 \over m}$$, then the (mn)th term o...
WB JEE 2008

## MCQ (More than One Correct Answer)

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In a certain test, there are n questions. In this test 2n-i students gave wrong answers to at least i questions, where i...
WB JEE 2020
Let x1, x2 be the roots of $${x^2} - 3x + a = 0$$ and x3, x4 be the roots of $${x^2} - 12x + b = 0$$. If {x_1} &lt; {x...
WB JEE 2019

## Subjective

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The harmonic mean of two numbers is 4. Their arithmetic mean A and the geometric mean G satisfy the relation 2A + G2 = 2...
WB JEE 2011
Find the sum of the first n terms of the series 0.2 + 0.22 + 0.222 + ......
WB JEE 2009

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