Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 40

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IMPORTANT

Earn 100

The first two terms of a geometric progression add up to $12$ . The sum of the third and the fourth terms is $48$ . If the terms of the geometric progression are alternately positive and negative, then the first term is

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Important Questions on Sequences and Series

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 41

The sum to infinity of

\frac{1}{7} + \frac{2}{7^{2}} + \frac{1}{7^{3}} + \frac{2}{7^{4}} + \dots

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 42

2.3 \bar{45}

in

\frac{p}{q}

form is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 43

The sum of

n

terms of the series

\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + . .

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 45

In an ordered set of four numbers, the first

3

are in

AP

and the last

3

are in

GP

whose common ratio is

\frac{7}{4}

. If the product of the first and fourth of these number is

49

, then the product of the second and third of these, is

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 46

Find the value of the positive integer

n

if

\frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \dots + \frac{1}{\sqrt{n} + \sqrt{n + 1}} = 5

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 47

What is the value of

$2100 - (x + 1) (x + 2006) [\frac{1}{(x + 1) (x + 2)} + \frac{1}{(x + 2) (x + 3)} + \dots + \frac{1}{(x + 2005) (x + 2006)}]$ ?

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 48

Let the sum

\sum_{n = 1}^{9} \frac{1}{n (n + 1) (n + 2)}

written in its lowest terms be

\frac{p}{q} .

Find the value of

q - p .

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 32

Let

a, b, c, d

and

e

be distinct positive numbers. If

a, b, c

and

\frac{1}{c}

,

\frac{1}{d}

,

\frac{1}{e}

both are in

AP

and

b, c, d

are in

GP

, then