Mathematics Crash Course KCET (UG)>Chapter 3 - Sequence and Series>Exercise 1>Q 80

EASY

KCET (UG)

IMPORTANT

Earn 100

If $a^{2} x^{4} + b^{2} y^{4} = c^{4},$ then the maximum value of $x y$ is

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Important Questions on Sequence and Series

MEDIUM

KCET (UG)

IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 3 - Sequence and Series>Exercise 1>Q 81

The value of the infinite product

6^{\frac{1}{2}} \times 6^{\frac{1}{2}} \times 6^{\frac{3}{8}} \times 6^{\frac{1}{4}} \times \dots

is

HARD

KCET (UG)

IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 3 - Sequence and Series>Exercise 1>Q 82

If

| x | < 1

, then

1 + 3 x + 5 x^{2} + 7 x^{3} + \dots

upto

\infty

is equal to

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KCET (UG)

IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 3 - Sequence and Series>Exercise 1>Q 83

The sum of numbers

1 + 2 \cdot 2 + 3 \cdot 2^{2} + 4 \cdot 2^{3} \dots + 100 \cdot 2^{99}

is

MEDIUM

KCET (UG)

IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 3 - Sequence and Series>Exercise 1>Q 84

If

tanθ = \sqrt{\frac{3}{2}}

, the sum of the infinite series

1 + 2 (1 - cosθ) + 3 {(1 - cosθ)}^{2} + 4 {(1 - cosθ)}^{3} + \dots . \infty

is

MEDIUM

KCET (UG)

IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 3 - Sequence and Series>Exercise 1>Q 85

Statement I If

x > 1,

then sum to infinite number of

1 + 3 (1 - \frac{1}{x}) + 5 {(1 - \frac{1}{x})}^{2} + 7 {(1 - \frac{1}{x})}^{3} + \dots

is

2 x^{2} - x

Statement II If

0 < y < 1,

then the sum of the series

1 + 3 y + 5 y^{2} + 7 y^{3} + \dots

is

\frac{1 + y}{(1 - y)^{2}}

MEDIUM

KCET (UG)

IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 3 - Sequence and Series>Exercise 1>Q 86

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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KCET (UG)

IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 3 - Sequence and Series>Exercise 1>Q 87

The sum of

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

is

MEDIUM

KCET (UG)

IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 3 - Sequence and Series>Exercise 1>Q 88

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

upto

10

terms

=