\( \Large \frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 10} + \frac{1}{10 \times 13} + \frac{1}{13 \times 16} = ? \)


A) \( \Large \frac{5}{16} \)

B) \( \Large \frac{3}{16} \)

C) \( \Large \frac{7}{16} \)

D) \( \Large \frac{11}{16} \)

Correct Answer:
A) \( \Large \frac{5}{16} \)

Description for Correct answer:
Given expression can be written as

\( \Large \frac{1}{3}\left[ \left(1-\frac{1}{4}\right) + \left(\frac{1}{4}-\frac{1}{7}\right) + \left(\frac{1}{7} - \frac{1}{10}\right) + \left(\frac{1}{10}-\frac{1}{13}\right) + \left(\frac{1}{13}-\frac{1}{16}\right) \right] \)

= \( \Large \frac{1}{3}\left[ 1 - \frac{1}{16} \right] = \frac{1}{3} \left(\frac{16-1}{16}\right) \)

= \( \Large \frac{1}{3} \times \frac{15}{16} = \frac{5}{16} \)

Part of solved Simplification questions and answers : >> Elementary Mathematics >> Simplification








Comments

No comments available




Similar Questions
1). \( \Large \left(2 -\frac{1}{3}\right) \left(2 - \frac{3}{5}\right) \left(2 - \frac{5}{7}\right)  \left(2 - \frac{997}{999}\right) \) is equal to
A). \( \Large \frac{1001}{999} \)
B). \( \Large \frac{999}{1001} \)
C). \( \Large \frac{1001}{3} \)
D). \( \Large \frac{5}{1001} \)
-- View Answer
2). The value of \( \Large \left(1 +\frac{1}{2}\right) \left(1 + \frac{1}{3}\right) \left(1 + \frac{1}{4}\right) \) ... \( \Large \left(1 + \frac{1}{150}\right) \) is
A). 65.5
B). 50.5
C). 105
D). 75.5
-- View Answer
3). If \( \Large x = \frac{\sqrt{3}}{2} \), then the value of \( \Large \frac{1+x}{1+\sqrt{1+x}} + \frac{1-x}{1-\sqrt{1-x }} \)
A). 0
B). 1
C). \( \Large \frac{\sqrt{3}}{2} \)
D). \( \Large \sqrt{3} \)
-- View Answer
4). If \( \Large x + \frac{1}{x} = 2 \), then \( \Large \frac{2x^{2} + 2}{3x^{2} + 5x + 3} \) = ?
A). \( \Large \frac{4}{11} \)
B). \( \Large \frac{1}{2} \)
C). \( \Large 1\frac{3}{4} \)
D). \( \Large 2\frac{1}{3} \)
-- View Answer
5). If \( \Large a + \frac{1}{b} = 1 \  and \  b + \frac{1}{c} = 1 \), then the value of \( \Large c + \frac{1}{a} = ? \)
A). 4
B). 24
C). 3
D). 1
-- View Answer


6). If \( \Large x + \frac{a}{x} = b \), then the value of \( \Large \frac{x^{2} + bx + a }{bx^{2} - x^{3}} \)
A). a + b
B). \( \Large \frac{2b}{a} \)
C). \( \Large \frac{b}{a} \)
D). ab
-- View Answer
7). If \( \Large x + \frac{1}{x} = 6 \), then \( \Large x^{4} + \frac{1}{x^{4}} \) is
A). 1152
B). 1154
C). 1148
D). 1150
-- View Answer
8). If \( \Large x + \frac{1}{x} = 3 \), then \( \Large x^{5} + \frac{1}{x^{5}} \) is equal to
A). 123
B). 83
C). 92
D). 112
-- View Answer
9). \( \Large 3x + 2y = 12 \) and \( \Large xy = 6 \), then the value of \( \Large 9x^{2} + 4y^{2} \) is
A). 76
B). 80
C). 72
D). 74
-- View Answer
10). A 120 m long rope is cut into 3 equal parts. What is the length of each part?
A). 40 m
B). 30 m
C). 50 m
D). 25 m
-- View Answer