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

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...