Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 4 - Progression and Series>DPP>Q 8

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IMPORTANT

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If $S_{n} = \frac{1 \cdot 2}{3!} + \frac{2 \cdot 2^{2}}{4!} + \frac{3 \cdot 2^{2}}{5!} + \dots +$ up to $n$ terms, then sum of infinite terms is:

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Important Questions on Progression and Series

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 4 - Progression and Series>DPP>Q 9

There is a certain sequence of positive real numbers. Beginning from the third term, each term of the sequence is the sum of all the previous terms. The seventh term is equal to

1000

and the first term is equal to

1

. The second term of this sequence is equal to:

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 4 - Progression and Series>DPP>Q 10

The sequence

\{x_{1}, x_{2} \dots x_{50}\}

has such a property that for each

k

,

x_{k}

is

k

less than the sum of other

49

numbers. The value of

96 x_{20}

is:

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 4 - Progression and Series>DPP>Q 11

Let

a_{0} = 0

and

a_{n} = 3 a_{n - 1} + 1

for

n \geq 1

. Then the remainder obtained on dividing

a_{2010}

by

11

is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 4 - Progression and Series>DPP>Q 12

Suppose

a_{1}, a_{2}, a_{3}, \dots, a_{2012}

are integers arranged in order on a circle. Each number is equal to the average of its two adjacent numbers. If the sum of all even indexed numbers is

3018

, What is the sum of all numbers?

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 4 - Progression and Series>DPP>Q 13

The sum of the series

\frac{9}{5^{2} \cdot 2 \cdot 1} + \frac{13}{5^{3} \cdot 3 \cdot 2} + \frac{17}{5^{4} \cdot 4 \cdot 3} + \dots

upto infinity: