Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 49

EASY

JEE Main/Advance

IMPORTANT

Earn 100

If $S$ denotes the sum to infinity and $S_{n}$ the sum of $n$ terms of the series $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + . . .,$ such that $S - S_{n} < \frac{1}{1000},$ then the least value of $n$ is

50% studentsanswered this correctly

Important Questions on Progression and Series

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 50

The first term of an infinite geometric series is

21 .

The second term and the sum of the series are both positive integers. Then which of the following is not the possible value of the second term

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 51

The sum of an infinite G.P. is

57

and the sum of their cubes is

9747

, then the common ratio of the G.P. is

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 52

If

S_{p}

denotes the sum of the series

1 + r^{p} + r^{2 p} + . . . . . . . . . . t o \infty

and

s_{p}

the sum of the series

1 - r^{p} + r^{2 p} - r^{3 p} + . . . . t o \infty, |r| < 1

, then

S_{p} + s_{p}

in terms of

S_{2 p}

is

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 53

If the sum to infinity of the series

1 + 2 r + 3 r^{2} + 4 r^{3} + . . . .

is

\frac{9}{4}

, then value of

r

is

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 54

The sum of series

1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + . . . . . \infty

is

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 55

The sum of

0.2 + 0.004 + 0.00006 + 0.0000008 + . . . . . t o \infty

is

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 56

The positive integer

n

for which

2 \times 2^{2} + 3 \times 2^{3} + 4 \times 2^{4} + . . . . + n \times 2^{n} = 2^{n + 10}

is

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 57

If

ω

is a complex n^th root of unity (

ω \neq 1

), then

\sum_{r = 1}^{n} (a r + b) ω^{r - 1}

is equal to