Practice Questions for Algebra - Progressions

1. CRE 5 - Miscellaneous | Algebra - Progressions

Find the sum of infinite terms of the series: 1 + 2x + 3x² + 4x³ + ... where |x| < 1.

(a)
x
(b)
1/(1 - x)²
(c)
1/(1 - x)
(d)
None of these

2. CRE 5 - Miscellaneous | Algebra - Progressions

Find the sum upto n terms of the series: 1 + 2x + 3x² + 4x³ + ...

(a)
nxⁿ
(b)
nxⁿ - $\frac{x^{n} - 1}{(x - 1)}$
(c)
$\frac{{nx}^{n}}{x - 1}$ - $\frac{x^{n} - 1}{{(x - 1)}^{2}}$
(d)
None of these

3. CRE 5 - Miscellaneous | Algebra - Progressions

Find the sum of infinite terms of the series: 1 + 4x + 9x² + 16x³ + ... where |x| < 1.

(a)
(1 + x)/(1 - x)³
(b)
(1 + x)/(1 - x)²
(c)
1/(1 - x)²
(d)
None of these

4. CRE 5 - Miscellaneous | Algebra - Progressions

Find the sum of the first 50 terms of the series $\frac{1}{1 \times 2}$ + $\frac{1}{2 \times 3}$ + $\frac{1}{3 \times 4}$ + ...

(a)
48/49
(b)
49/50
(c)
50/51
(d)
1/49
(e)
None of these

5. CRE 5 - Miscellaneous | Algebra - Progressions

Find the sum of the first 50 terms of the series $\frac{1}{1 \times 3}$ + $\frac{1}{3 \times 5}$ + $\frac{1}{5 \times 7}$ + ...

(a)
100/101
(b)
50/101
(c)
49/99
(d)
None of these

6. CRE 5 - Miscellaneous | Algebra - Progressions

Find the sum of first 50 terms of the series: $\frac{1}{1 \times 2 \times 3}$ + $\frac{1}{2 \times 3 \times 4}$ + $\frac{1}{3 \times 4 \times 5}$ + ...

(a)
$(\frac{1}{1 \times 2} - \frac{1}{49 \times 50})$
(b)
$\frac{1}{2} (\frac{1}{1 \times 2} - \frac{1}{51 \times 52})$
(c)
$\frac{1}{2} (\frac{1}{49 \times 50})$
(d)
None of these

7. CRE 5 - Miscellaneous | Algebra - Progressions

Find the sum of first 50 terms of the series $\frac{1}{2^{2} - 1}$ , $\frac{1}{4^{2} - 1}$ , $\frac{1}{6^{2} - 1}$ , ...

(a)
100/101
(b)
50/101
(c)
49/99
(d)
None of these

8. CRE 5 - Miscellaneous | Algebra - Progressions

1 × 1! + 2 × 2! + 3 × 3! + 4 × 4! + ⋯ 10 × 10! = ?

(a)
11!
(b)
11! - 1
(c)
11! - 10!
(d)
10! + 1
(e)
None of these

9. CRE 5 - Miscellaneous | Algebra - Progressions

Find the sum of first 20 terms of the series: 1, 3, 6, 10, ...

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

10. CRE 5 - Miscellaneous | Algebra - Progressions

Find the sum of first 10 terms of the series: $\frac{1}{2}$ + $\frac{1}{2 + 4}$ + $\frac{1}{2 + 4 + 6}$ + ...

(a)
1
(b)
1/11
(c)
10/11
(d)
12/11
(e)
None of these

11. CRE 5 - Miscellaneous | Algebra - Progressions

If sum of n terms of a series is defined as S_n = n² + n + 1, then find the 15^th term of this series.

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

12. CRE 5 - Miscellaneous | Algebra - Progressions

If T_n = n² + n + 1, then find the sum of first 10 terms of this series.

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

13. CRE 5 - Miscellaneous | Algebra - Progressions

Find the sum of the following series: 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ⋯ + 9 × 10

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

CRE 5 - Miscellaneous | Algebra - Progressions

Feedback