Sequence and Series · Mathematics · WB JEE

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 of the A.P. is...

The sum of the series $$(1 + 2) + (1 + 2 + {2^2}) + (1 + 2 + {2^2} + {2^3}) + ....$$ upto n terms is

The 5th term of the series $${{10} \over 9},{1 \over 3}\sqrt {{{20} \over 3}} ,{2 \over 3}$$ is

If a, b, c be in Arithmetic progression, then the value of $$(a + 2b - c)(2b + c - a)(a + 2b + c)$$ is

If three real numbers a, b, c are in Harmonic Progression, then which of the following is true?

The sum of the infinite series $${\left( {{1 \over 3}} \right)^2} + {1 \over 3}{\left( {{1 \over 3}} \right)^4} + {1 \over 5}{\left( {{1 \over 3}} \ri...

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 in...

If three positive real numbers a, b, c are in A.P. and abc = 4 then the minimum possible value of b is

For what value of m, $${{{a^{m + 1}} + {b^{m + 1}}} \over {{a^m} + {b^m}}}$$ is the arithmetic mean of a and b?

The coefficient of xn, where n is any positive integer, in the expansion of (1 + 2x + 3x2 + ....... $$\infty$$)1/2 is...

The sum of the infinite series $$1 + {1 \over {2!}} + {{1\,.\,3} \over {4!}} + {{1\,.\,3\,.\,5} \over {6!}} + \,....$$ is

If sum of an infinite geometric series is $${4 \over {3}}$$ and its 1st term is $${3 \over {4}}$$, then its common ratio is

Sum of n terms of the following series 13 + 33 + 53 + 73 ......... is

G.M. and H.M. of two numbers are 10 and 8 respectively. The numbers are

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

If angles A, B and C are in A.P., then $${{a + c} \over b}$$ is equal to

The value of $${2 \over {3!}} + {4 \over {5!}} + {6 \over {7!}} + $$ ............ is

The value of $$\sum\limits_{r = 2}^\infty {{{1 + 2 + .... + (r - 1)} \over {r!}}} $$

Given an A.P. and a G.P. with positive terms, with the first and second terms of the progressions being equal. If $$a_n$$ and $$b_n$$ be the $$n^{\tex...

If for the series $$a_1, a_2, a_3$$, ...... etc, $$\mathrm{a}_{\mathrm{r}}-\mathrm{a}_{\mathrm{r}+\mathrm{i}}$$ bears a constant ratio with $$\mathrm{...

If $$\alpha_1, \alpha_2, \ldots, \alpha_n$$ are in A.P. with common difference $$\theta$$, then the sum of the series $$ \sec \alpha_1 \sec \alpha_2+\...

If the n terms $${a_1},{a_2},\,......,\,{a_n}$$ are in A.P. with increment r, then the difference between the mean of their squares & the square of th...

If $$1,{\log _9}({3^{1 - x}} + 2),{\log _3}({4.3^x} - 1)$$ are in A.P., then x equals

Consider a quadratic equation $$a{x^2} + 2bx + c = 0$$ where a, b, c are positive real numbers. If the equation has no real root, then which of the fo...

Let $${a_1},{a_2},{a_3},\,...,\,{a_n}$$ be positive real numbers. Then the minimum value of $${{{a_1}} \over {{a_2}}} + {{{a_2}} \over {{a_3}}}\, + \,...

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 lengths of the sides of a tri...

Let $${a_n} = {({1^2} + {2^2} + .....\,{n^2})^n}$$ and $${b_n} = {n^n}(n!)$$. Then

Let a, b, c be real numbers, each greater than 1, such that $${2 \over 3}{\log _b}a + {3 \over 5}{\log _c}b + {5 \over 2}{\log _a}c = 3$$. If the valu...

Consider the real valued function h : {0, 1, 2, ...... 100} $$\to$$ R such that h(0) = 5, h(100) = 20 and satisfying h(p) = $${1 \over 2}$$ {h(p + 1) ...

The digit in the unit's place of the number 1! + 2! + 3! + .... + 99! is

Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while $$\log \left( {{{5c} \over {2a}}} \right),\log \left( {{{7b} \over {5c}...

If a and b are arbitrary positive real numbers, then the least possible value of $${{6a} \over {5b}} + {{10b} \over {3a}}$$ is

Let I(n) = nn, J(n) = 13.5 ......... (2n $$ - $$ 1) for all (n > 1), n $$ \in $$ N, then

Given that n numbers of arithmetic means are inserted between two sets of numbers a, 2b and 2a, b where a, b $$ \in $$ R. Suppose further that the mth...

In a GP series consisting of positive terms, each term is equal to the sum of next two terms. Then, the common ratio of this GP series is

If a, x are real numbers and | a | < 1, | x | < 1, then 1 + (1 + a) x + (1 + a + a2) x2 + ..... $$\infty $$ is equal to

The sum of n terms of the following series $${1^3} + {3^3} + {5^3} + {7^3} + ...$$ is

Find the sum of the first n terms of the series 0.2 + 0.22 + 0.222 + ......

The harmonic mean of two numbers is 4. Their arithmetic mean A and the geometric mean G satisfy the relation 2A + G2 = 27. Find the numbers....

In a certain test, there are n questions. In this test 2n-i students gave wrong answers to at least i questions, where i = 1, 2, ..., n. If the total ...

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 $${x_1} < {x_2} < {x_3} < {x_4}$$ an...