The sum of the series 1- 2 3 1 8 - 2- 5 3- 6 1 8 2 - 2- 5- 8 3- 6- 9 1 8 3 - is

The correct option is A 4 √( 49 ) Consider this series third term as #160; ( 23 1)×( 23 2) ×( 23 3)3× 2× 1(18)^3 ( n 1)×( n 2) × ( n ...

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Standard X

Mathematics

Sum of n Terms

The sum of th...

Question

The sum of the series
$1 + \frac{2}{3} (\frac{1}{8}) + \frac{2 \times 5}{3 \times 6} {(\frac{1}{8})}^{2} + \frac{2 \times 5 \times 8}{3 \times 6 \times 9} {(\frac{1}{8})}^{3} + . . . .$ is

\frac{4}{\sqrt[3]{49}}

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\frac{\sqrt[3]{49}}{4}

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\frac{4}{\sqrt[3]{81}}

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\frac{\sqrt[3]{81}}{4}

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Solution

The correct option is A $\frac{4}{\sqrt[3]{49}}$
Consider this series third term as
$\frac{(- \frac{2}{3} - 1) \times (- \frac{2}{3} - 2) \times (- \frac{2}{3} - 3)}{3 \times 2 \times 1} {(\frac{1}{8})}^{3}$

$\frac{(- n - 1) \times (- n - 2) \times (- n - 3)}{3 \times 2 \times 1} (x)^{3}$
Hence this term seems like the third term in the expansion of $(1 - x)^{- n}$

So,
here $x = \frac{1}{8}$ and $- \frac{2}{3}$ plays the role of $- n$ here

Hence ${(1 - \frac{1}{8})}^{- \frac{2}{3}}$ must be the answer

Therefore Answer is $\frac{4}{\sqrt[3]{49}}$

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Similar questions

Express the exponential form with prime number as base.

(1) 4

(2) 8

(3) 16

(4) 49

(5) 81

Solve:

(i) $2 - \frac{3}{5}$

(ii) $4 + \frac{7}{8}$

(iii) $\frac{3}{5} + \frac{2}{7}$

(iv) $\frac{9}{11} - \frac{4}{15}$

(v) $\frac{7}{10} + \frac{2}{5} + \frac{3}{2}$

(vi) $2 \frac{2}{3} + 3 \frac{1}{2}$

(vii) $8 \frac{1}{2} - 3 \frac{5}{8}$

Q. Calculate 1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + ... + 49 − 50.

Prove that :

$(i) (\sqrt{3 \times 5^{- 3}} \div \sqrt[3]{3^{- 1}} \sqrt{5}) \times \sqrt[6]{3 \times 5^{6}} = \frac{3}{5} (i i) 9^{\frac{3}{2}} - 3 \times 5^{0} - {(\frac{1}{81})}^{\frac{- 1}{2}} = 15 (i i i) {(\frac{1}{4})}^{- 2} - 3 \times 8^{\frac{2}{3}} \times 4^{0} + {(\frac{9}{16})}^{\frac{- 1}{2}} = \frac{16}{3} (i v) \frac{2^{\frac{1}{2}} \times 3^{\frac{1}{3}} \times 4^{\frac{1}{4}}}{10^{\frac{- 1}{5}} \times 5^{\frac{3}{5}}} \div \frac{3^{\frac{4}{3}} \times 5^{\frac{- 7}{5}}}{4^{\frac{- 3}{5}} \times 6} = 10 (v) \sqrt{\frac{1}{4}} + (0.01)^{\frac{- 1}{2}} - (27)^{\frac{2}{3}} = \frac{3}{2} (v i) \frac{2^{n} + 2^{n - 1}}{2^{n + 1} - 2^{n}} = \frac{3}{2} (v i i) {(\frac{64}{125})}^{\frac{- 2}{3}} + \frac{1}{{(\frac{256}{625})}^{\frac{1}{4}}} + {(\frac{\sqrt{25}}{\sqrt[3]{64}})}^{0} = \frac{61}{16} (v i i i) \frac{3^{- 3} \times 6^{2} \times \sqrt{98}}{5^{2} \times \sqrt[3]{\frac{1}{25}} \times (15)^{\frac{- 4}{3}} \times 3^{\frac{1}{3}}} = 28 \sqrt{2} (i x) \frac{(0.6)^{0} - (0.1)^{- 1}}{{(\frac{3}{8})}^{- 1} {(\frac{3}{2})}^{3} + {(\frac{1}{3})}^{- 1}} = - \frac{3}{2}$

Q. Write the degree of the following polynomials.

(1) 64p³ − 10p
(2) 8n² − 25n + 9
(3) x − 11 + 3x⁴
(4) 39m
(5) 81
(6) 2n⁵ − n³ + 6 − 7n²
(7) 9a⁵ − 61
(8)

\frac{5}{11} x - x^{4}

(9) 0

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The sum of the series1+23(18)+2×53×6(18)2+2×5×83×6×9(18)3+.... is

The sum of the series
$1 + \frac{2}{3} (\frac{1}{8}) + \frac{2 \times 5}{3 \times 6} {(\frac{1}{8})}^{2} + \frac{2 \times 5 \times 8}{3 \times 6 \times 9} {(\frac{1}{8})}^{3} + . . . .$ is