The sum of the series 3 4- 8 - 3- 5 4- 8- 12 - 3- 5- 7 4- 8- 12- 16 - is

The correct option is B √( 2 3 ) 3 4 3 4.8 3,5 4.8.12 + 3.5.7 4.8.12.16 ....+ 3 4 3 4 =1 1 4 + 1.3 2.4.4 1.3.5 4.4.34. ...

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Standard XII

Mathematics

Property 2

The sum of th...

Question

The sum of the series
$\frac{3}{4 \cdot 8} - \frac{3 \cdot 5}{4 \cdot 8 \cdot 12} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12 \cdot 16} - . . . . . .$ is

\sqrt{\frac{3}{2}} - \frac{3}{4}

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\sqrt{\frac{2}{3}} - \frac{3}{4}

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\sqrt{\frac{3}{2}} - \frac{1}{4}

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\sqrt{\frac{2}{3}} - \frac{1}{4}

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Solution

The correct option is B $\sqrt{\frac{2}{3}} - \frac{3}{4}$
$\frac{3}{4.8} - \frac{3, 5}{4.8.12} + \frac{3.5.7}{4.8.12.16} - . . . . + \frac{3}{4} - \frac{3}{4}$
$= 1 - \frac{1}{4} + \frac{1.3}{2.4.4} - \frac{1.3.5}{4.4.34.2.} + . . . - \frac{3}{4}$
$= [1 + \frac{1}{1!} (- \frac{1}{4}) + \frac{1 (1 + 2)}{2!} {(- \frac{1}{4})}^{2} + \frac{1 (1 + 2) (1 + 4)}{3!} {(- \frac{1}{4})}^{3} + . . .] - \frac{3}{4}$
$= {(1 - \frac{1}{4})}^{- 1 / 2} - \frac{3}{4} = \sqrt{\frac{2}{3}} - \frac{3}{4}$

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Similar questions

Fill in the blanks:

$(i) - 4 \times \frac{7}{9} = \frac{7}{9} \times$ ___

$(i i) \frac{5}{11} \times \frac{- 3}{8} = \frac{- 3}{8} \times$ ___

$(i i i) \frac{1}{2} \times (\frac{3}{4} + \frac{- 5}{12}) = \frac{1}{2} \times$ ____ $+ (\times) \frac{- 5}{12}$

$(i v) \frac{- 4}{5} \times \frac{5}{7} \times$ ___ $= (\frac{- 4}{5} \times \frac{5}{7}) \times \frac{- 8}{9}$

Simplify the following

(a) 12 + [{1 + (15 − 3)} × 4]

(b)

(c)

(d)

(e)

Evaluate :

$(i) \frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9} (i i) \frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5} (i i i) \frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{9} (i v) \frac{3}{8} + \frac{- 5}{12} + \frac{3}{7} + \frac{3}{12} + \frac{- 5}{8} + \frac{- 2}{7}$

Find the value of:

(i) $(- 4) \div \frac{2}{3}$

(ii) $\frac{- 3}{5} \div 2$

(iii) $\frac{- 4}{5} \div - 3$

(iv) $\frac{- 1}{8} \div \frac{3}{4}$

(v) $\frac{- 2}{13} \div \frac{1}{7}$

(vi) $\frac{- 7}{12} \div \frac{- 2}{13}$

(vii) $\frac{3}{13} \div \frac{- 4}{65}$

Q. Find the value of:

(1) 3⁶
(2) 6³
(3) 2⁶
(4) 1⁸
(5) 5⁴
(6) 4³
(7) 10⁵
(8) 10⁷
(9) 7⁴
(10) 8²

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The sum of the series34⋅8−3⋅54⋅8⋅12+3⋅5⋅74⋅8⋅12⋅16−...... is

The correct option is B √23−3434.8−3,54.8.12+3.5.74.8.12.16−....+34−34=1−14+1.32.4.4−1.3.54.4.34.2.+...−34=[1+11!(−14)+1(1+2)2!(−14)2+1(1+2)(1+4)3!(−14)3+...]−34=(1−14)−1/2−34=√23−34

The sum of the series
$\frac{3}{4 \cdot 8} - \frac{3 \cdot 5}{4 \cdot 8 \cdot 12} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12 \cdot 16} - . . . . . .$ is