Embibe Experts Solutions for Chapter: Sequences and Series, Exercise 3: EXERCISE-3

If the sum of the series, $7+77+777+\dots \dots$ to $n$ terms is $S=(a/b)\left({10}^{n+1}-9n-10\right)$, then $a+b$ (where $a\& b$ are coprime numbers) is equal to

Let one AM '$a$' & two GM's $p\&q$ be inserted between any two given numbers, if $p^3+q^3=kapq$ , then $k$ is equal to

Given $a, b, c$ three numbers and the sum of numbers is $25$. The numbers $2,a, b$ are in A.P. and the numbers $b,c,18$ are consecutive terms of a G.P., then the value of $\left(a+\frac{c}{b}\right)$ is equal to

Find the sum of the first $8$ terms of the series: $1+2\left(1+\frac{1}{n}\right)+3{\left(1+\frac{1}{n}\right)}^2+4{\left(1+\frac{1}{n}\right)}^3+\dots \dots ...$

The harmonic mean of two numbers is $4$ . The arithmetic mean $A$ and  the geometric mean $G$ satisfy the relation $2 A+G^2=27$. The sum of squares of those two numbers is

Let $a, b, c$ are sides of a scalene triangle, if $(a+b+c{)}^3>k(a+b-c\left)\right(b+c-a\left)\right(c+a-b)$, then the value of $k$. is

Let the value of $x+y+z$ is $15$, if $a, x, y, z, b$ are in A.P. while the value of $;(1 / x)+(1 / y)+(1 / z)$ is $5 / 3$ if $a, x, y, z, b$ are in H.P, then value of $\left(a^2+b^2\right)$ is

If in a G.P., the ratio of the sum of the first eleven terms to the sum of the last eleven terms is $\frac{1}{8}$ and the ratio of the sum of all the terms without the first nine to the sum of all the terms without the last nine is $2$, then the number of terms in the G.P is: