Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 74

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IMPORTANT

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Consider the sequence $1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, \dots \dots$ Then $1025^{th}$ term will be

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Important Questions on Progression and Series

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 75

The value of

\sum_{i = 1}^{n} \sum_{j = 1}^{i} \sum_{k = 1}^{j} 1 = 220

, then the value of

n

equals

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 76

If

1^{2} + 2^{2} + 3^{2} + . . . + 2003^{2} = (2003) (4007) (334)

and

(1) (2003) + (2) (2002) + (3) (2001) + . . . + (2003) (1) = (2003) (334) (x)

, then

x

equals

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 77

If

t_{n}

denotes the

n

th term of the series

2 + 3 + 6 + 11 + 18 + . . .

then

t_{50}

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 78

The sum of series

\sum_{r = 0}^{r} {(- 1)}^{r} {(n + 2 r)}^{2}

(where

n

is even) is

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 79

If

(1^{2} - t_{1}) + (2^{2} - t_{2}) + . . . + (n^{2} - t_{n}) = \frac{n (n^{2} - 1)}{3}

, then

t_{n}

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 80

If

(1 + 3 + 5 + . . . + p) + (1 + 3 + 5 + . . . . + q) = (1 + 3 + 5 + . . . + r)

where each set of parentheses contains the sum of consecutive odd intergers as shown, the smallest possible value of

p + q + r

(where

p > 6

) is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 81

If

H_{n} = 1 + \frac{1}{2} + . . . + \frac{1}{n}

, then the value of

S_{n} = 1 + \frac{3}{2} + \frac{5}{3} + . . . . + \frac{99}{50}

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 82

The sum to

50

terms of the series

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

is