Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 17

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IMPORTANT

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Let $S_{k}$ be the sum of an infinite $G . P .$ whose first terms is $' k'$ and common ratio is $\frac{1}{k + 1} .$ Then $\sum_{k = 1}^{10} S_{k}$ is equal to

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Important Questions on Progression and Series

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 18

The value of the sum

\sum_{i = 1}^{20} i (\frac{1}{i} + \frac{1}{i + 1} + \frac{1}{i + 2} + . . . + \frac{1}{20})

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 19

The difference between the sum of the first

k

terms of the series

1^{3} + 2^{3} + 3^{3} + . . . + n^{3}

and the sum of the first

k

terms of

1 + 2 + 3 + . . . + n

is

1980 .

The value of

k

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 20

The value of the

\sum_{n = 0}^{\infty} \frac{2 n + 3}{3^{n}}

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 21

The sum of the infinite Arithmetic-Geometric progression

3, 4, 4, . . . \infty

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 22

\sum_{r = 1}^{50} \frac{r^{2}}{r^{2} + {(51 - r)}^{2}}

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 23

If

\sum_{r = 0}^{100} \frac{1}{2^{r} + 2^{50}} = \frac{n}{2^{50}},

then the value of

n

is

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 24

Let

<a_{n}>

be an arithmetic sequence of

99

terms such that sum of its odd numbered terms is

1000

, then the value of

\sum_{r = 1}^{50} {(- 1)}^{\frac{r (r + 1)}{2}} \cdot a_{2 r - 1}

is

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 25

If the sum of $n$ terms of the series

$\frac{2 n + 1}{2 n - 1} + 3 {(\frac{2 n + 1}{2 n - 1})}^{2} + 5 {(\frac{2 n + 1}{2 n - 1})}^{3} + . . .$ is $820$ , then the value of $n$ is