Sequences and Series · Mathematics · COMEDK

Consider an infinite geometric series with first term '$$a$$' and common ratio '$$r$$'. If the sum of infinite geometric series is 4 and the second term is $$\frac{3}{4}$$ then

If two positive numbers are in the ratio $$3+2 \sqrt{2}: 3-2 \sqrt{2}$$, then the ratio between their A.M (arithmetic mean) and G.M (geometric mean) is

A number consists of three digits in geometric progression. The sum of the right hand and left hand digits exceeds twice the middle digit by 1 and the sum of left hand and middle digits is two third of the sum of the middle and right hand digits. Then the sum of digits of number is

A geometric progression consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then the common ratio of the G.P is

Given $$a, b, c$$ are three unequal numbers such that $$\mathrm{b}$$ is arithmetic mean of $$a$$ and $$c$$ and $$(b-a),(c-b), a$$ are in geometric progression. Then $$a: b: c$$ is

$$ (32) \times(32)^{\frac{1}{6}} \times(32)^{\frac{1}{36}} \times-----\infty \text { is equal to } $$

The sum of $$n$$ terms of the series, $$\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+\ldots$$ is

The value of $$\frac{1}{2 !}+\frac{2}{3 !}+\ldots+\frac{99}{100 !}$$ is equal to

If the sum of 12th and 22nd terms of an AP is 100, then the sum of the first 33 terms of an $$\mathrm{AP}$$ is

If three numbers $$a, b, c$$ constitute both an A.P and G.P, then

Le $$x$$ be the arithmetic mean and $$y, z$$ be the two geometric means between any two positive numbers, then $$\frac{y^3+z^3}{x y z}=$$ -----------

If $$S = {{{2^2} - 1} \over 2} + {{{3^2} - 2} \over 6} + {{{4^2} - 3} \over {12}}\, + \,...$$ upto 10 terms, then S is equal to

The first and fifth terms of an A.P. are $$-14$$ and 2 respectively and the sum of its n terms is 40. The value of n is

Total number of elements in the power set of A containing 17 elements is

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

If a, b, c are in A.P., $$b-a,c-b$$ and a are in G.P., then a : b : c is

$${1 \over {2\,.\,5}} + {1 \over {5\,.\,8}} + {1 \over {8\,.\,11}} + ............. + {1 \over {(3n - 1)(3n + 2)}} = $$