Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 25

EASY

JEE Advanced

IMPORTANT

Earn 100

The sum of the series $1 + \frac{1}{4 \cdot 2!} + \frac{1}{16 \cdot 4!} + \frac{1}{64 \cdot 6!} + . . .$ is

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Important Questions on Sequence and Series

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 26

Let

T_{r}

be the

r th

term of an

AP

, whose first term is

a

and common difference is

d

. If for some positive integers

m, n, m \neq n, T_{m} = \frac{1}{n}

and

T_{n} = \frac{1}{m}

, then

a - d

equals

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 27

The sum of the first

n

terms of the series

1^{2} + 2 \cdot 2^{2} + 3^{2} + 2 \cdot 4^{2} + 5^{2} + 2 \cdot 6^{2} + \dots

is

\frac{n {(n + 1)}^{2}}{2}

where

n

is even. When

n

is odd, then the sum is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 28

The sum of the series

\frac{1}{2!} + \frac{1}{4!} + \frac{1}{6!} + \dots

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 29

The sum of the series

\frac{1}{1 \cdot 2} - \frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} - \dots

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 30

If

1, \log_{3} \sqrt{(3^{1 - x} + 2)}, \log_{3} (4 \cdot 3^{x} - 1)

are in

AP

. Then,

x

equals

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 31

The value of

2^{1 / 4} \cdot 4^{1 / 8} \cdot 8^{1 / 16} \dots

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 32

If the

5

th term of a

GP

is

2

, then the product of its

9

terms is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Entrances Gallery>Q 33

\sum_{n = 0}^{\infty} \frac{{(\log_{e} x)}^{n}}{n!}

is equal to