1-4-1-1-2 -1-3-4 -1-5-4 -1-7-4 is equal to-

The correct options are C 255/948 D 945/256 1/4× (1 +1/2) × (1 +3/4) × (1 +5/4) × (1 +7/4) = 1/4 ×3/2×7/4×9/4×11/4 = 2079/512 Also, 2079/512 =2079 × 2/512 × 2 ...

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Byju's Answer

Standard VI

Mathematics

Subtraction of like Fractions

1/4×1+1/2 ×1+...

Question

$\frac{1}{4} \times (1 + \frac{1}{2}) \times (1 + \frac{3}{4}) \times (1 + \frac{5}{4}) \times (1 + \frac{7}{4}$ ) is equal to:

44/256

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948/255

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255/948

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945/256

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Solution

The correct options are
C
255/948

D
945/256

$\frac{1}{4} \times (1 + \frac{1}{2}) \times (1 + \frac{3}{4}) \times (1 + \frac{5}{4}) \times (1 + \frac{7}{4}$ )

= $\frac{1}{4} \times \frac{3}{2} \times \frac{7}{4} \times \frac{9}{4} \times \frac{11}{4} = \frac{2079}{512}$
Also, $\frac{2079}{512} = \frac{2079 \times 2}{512 \times 2} = \frac{4158}{1024}$

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Similar questions

\frac{\frac{1}{2!} + \frac{1}{4!} + \frac{1}{6!} + . . . \infty}{1 + \frac{1}{3!} + \frac{1}{5!} + \frac{1}{7!} + . . . \infty}

is equal to

Q. The value of

\frac{1}{1 \cdot 2 \cdot 3} + \frac{1}{2 \cdot 3 \cdot 4} + \frac{1}{3 \cdot 4 \cdot 5} + \frac{1}{4 \cdot 5 \cdot 6}

is equal to

Q. If

U = 1, 2, 3, 4, 5, 6, 7, A = 1, 2, 3, 4, 5

, and

B = 1, 3, 5, 7

, then

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is equal to:

Q. Sum of the series

1 (1) + 2 (1 + 3) + 3 (1 + 3 + 5) + 4 (1 + 3 + 5 + 7) + . . . . + 10 (1 + 3 + 5 + 7 + . . . . + 19)

is equal to

Question 22

Which of the following is an example of distributive property of multiplication over addition for rational numbers.
(a) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = [- \frac{1}{4} \times \frac{2}{3}] + [- \frac{1}{4} \times (\frac{- 4}{7})]$
(b) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = [\frac{1}{4} \times \frac{2}{3}] - (\frac{- 4}{7})$
(c) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = \frac{2}{3} + (- \frac{1}{4}) \times \frac{- 4}{7}$
(d) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = {\frac{2}{3} + (\frac{- 4}{7})} - \frac{1}{4}$

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14×(1+12)×(1+34)×(1+54)×(1+74) is equal to:

The correct options are C 255/948 D 945/256 14×(1+12)×(1+34)×(1+54)×(1+74) = 14 ×32×74×94×114=2079512 Also, 2079512=2079×2512×2=41581024

$\frac{1}{4} \times (1 + \frac{1}{2}) \times (1 + \frac{3}{4}) \times (1 + \frac{5}{4}) \times (1 + \frac{7}{4}$ ) is equal to: