Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 21

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If $10$ harmonic means $H_{1}, H_{2}, H_{3} \dots \dots . H_{10}$ are inserted between $7$ and $- \frac{1}{3}$ , then -

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Important Questions on Sequences and Series

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 23

Indicate the correct alternative(s), for

0 < ϕ < \frac{π}{2}

, if

x = \sum_{n = 0}^{\infty} \cos^{2 n} ϕ, y = \sum_{n = 0}^{\infty} \sin^{2 n} ϕ

and

z = \sum_{n = 0}^{\infty} \cos^{2 n} ϕ \sin^{2 n} ϕ

. then

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 24

If

x_{1}, x_{2}, x_{3}

as well as

y_{1}, y_{2}, y_{3}

are in

G . P .

with the same common ratio, then the points

(x_{1}, y_{1}), (x_{2}, y_{2})

and

(x_{3}, y_{3})

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-3>Q 12

If there are

n

AM's between

1 & 31

such that

7 t h

mean :

(n - 1)

th mean

= 5 : 9

, then value of

n

is

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-3>Q 13

If the sum of the series,

7 + 77 + 777 + \dots \dots

to

n

terms is

S = (a / b) (10^{n + 1} - 9 n - 10)

, then

a + b

(where

a & b

are coprime numbers) is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-3>Q 14

Let one AM '

a

' & two GM's

p & q

be inserted between any two given numbers, if

p^{3} + q^{3} = k a p q

, then

k

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-3>Q 17

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 $(a + \frac{c}{b})$ is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-3>Q 18

Find the sum of the first

8

terms of the series:

1 + 2 (1 + \frac{1}{n}) + 3 {(1 + \frac{1}{n})}^{2} + 4 {(1 + \frac{1}{n})}^{3} + \dots \dots . . .

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-3>Q 19

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