Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 9

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If $\log_{2} (a + b) + \log_{2} (c + d) \geq 4$ . Then the min. value of the expression $a + b + c + d$ is -

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Important Questions on Sequences and Series

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 10

The minimum value of

4^{x} + 4^{1 - x}, x \in R,

is

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 11

If

a_{n} > 1

for all

n \in N

then

\log_{a_{2}} a_{1} + \log_{a_{3}} a_{2} + \dots + \log_{a_{n}} a_{n - 1} + \log_{a_{1}} a_{n}

has the minimum value

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 12

The minimum value of

\frac{x^{4} + y^{4} + z^{4}}{x y z}

for positive reals

x, y, z

is

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 13

If

α \in (0, \frac{π}{2})

, then

\sqrt{x^{2} + x} + \frac{\tan^{2} α}{\sqrt{x^{2} + x}}

is always greater than or equal to

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 14

The minimum value of

p x + q y

where

x y = r^{2}

is

(p > 0, q > 0, r > 0)

-

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 15

$x, y and z$ are positive integers, then the value of expression $(x + y) (y + z) (z + x)$ is

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 1

If the sum of the first

15

terms of the series

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

is equal to

225 K

, then

K

is equal to :

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 8 - Sequences and Series>Exercise>Q 2

Sum of

n

terms of the series

2^{3} + 4^{3} + 6^{3} + \dots

is

3528

, then

n

is