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

HARD

JEE Main/Advance

IMPORTANT

Earn 100

Sum of an infinite G.P. is $2$ and sum of its first two terms is $1$ . If its second terms is negative, then which of the following is/are true?

100% studentsanswered this correctly

Important Questions on Progression and Series

HARD

JEE Main/Advance

IMPORTANT

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

For

0 < ϕ < π / 2

, if

x = \sum_{n = 0}^{\infty} \cos^{2 n} ϕ, y = \sum_{n = 0}^{\infty} \sin^{2 n} ϕ

and

z = \sum_{n = 0}^{\infty} \cos^{2 n} ϕ \sin^{2 n} ϕ

then

HARD

JEE Main/Advance

IMPORTANT

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

For the series,

S = 1 + \frac{1}{(1 + 3)} {(1 + 2)}^{2} + \frac{1}{(1 + 3 + 5)} {(1 + 2 + 3)}^{2} + \frac{1}{(1 + 3 + 5 + 7)} {(1 + 2 + 3 + 4)}^{2} + . . .

HARD

JEE Main/Advance

IMPORTANT

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

If

\sum_{r = 1}^{n} r (r + 1) (2 r + 3) = a n^{4} + b n^{3} + c n^{2} + d n + e

, then

HARD

JEE Main/Advance

IMPORTANT

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

If

S_{n} = 1^{2} - 2^{2} + 3^{2} - 4^{2} + 5^{2} - 6^{2} + . . . .,

then

HARD

JEE Main/Advance

IMPORTANT

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

\frac{1}{\sqrt{2} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{11}} + . . . . n

terms is equal to

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 26

In the 20th row of the triangle

1

2 3

4 5 6

$⋰$ $⋮$ $⋱$

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 27

Given that

x + y + z = 15

when

a, x, y, z, b

are in A.P. and

\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{5}{3}

when

a, x, y, z, b

are in H.P. Then

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 28

If

a, b,

and

c

are in H.P.., then the value of

\frac{(a c + a b - b c) (a b + b c - a c)}{{(a b c)}^{2}}

is