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

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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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Important Questions on Sequences and Series

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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 1>Q 49

The sum of

n

terms of an A.P. is

an (n - 1)

. The sum of the squares of these terms is equal to

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 50

The sum of

(31)^{2} + (32)^{2} + (33)^{2} + \dots . + (60)^{2}

is

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 51

The sum of

n

terms of the following series

1.2 + 2.3 + 3.4 + 4.5 + \dots \dots . .

will be

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 52

2 \cdot 1^{2} + 3 \cdot 2^{2} + 4 \cdot 3^{2} + \dots .

upto

10

terms

=

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 53

The sum of

\frac{1}{2 \times 3 \times 4} + \frac{1}{3 \times 4 \times 5} + \frac{1}{4 \times 5 \times 6} + \dots + \frac{1}{13 \times 14 \times 15} + \frac{1}{14 \times 15 \times 16}

is

\frac{m}{n}

in its lowest terms. Find the
value of

n - 5 m