The correct option is C 4251^3 2^3 + 3^3 4^3 +....+ 9^3 = 1^3 + 2^3 + 3^3 + 4^3 +....+ 9^3 2(2^3 + 4^3 + 6^3 + 8^3) = ( 9 × 10/2 ) 16 (1^3 + 2^3 + 3 ...

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Byju's Answer

Standard XII

Mathematics

Summation by Sigma Method

13-23+33-43+…...

Question

$1^{3} - 2^{3} + 3^{3} - 4^{3} + . . . . + 9^{3} =$

425

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-425

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475

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-475

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Solution

The correct option is A 425
$1^{3} - 2^{3} + 3^{3} - 4^{3} + . . . . + 9^{3} = 1^{3} + 2^{3} + 3^{3} + 4^{3} + . . . . + 9^{3} - 2 (2^{3} + 4^{3} + 6^{3} + 8^{3}) = (\frac{9 \times 10}{2}) - 16 (1^{3} + 2^{3} + 3^{3} + 4^{3}) = 45^{2} - 16 {(\frac{4 \times 5}{2})}^{2} = 45^{2} - 40^{2} = 425$

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Similar questions

1^{3} - 2^{3} + 3^{3} - 4^{3} + . . . + 9^{3}

equals

Q. Find:

1^{3} - 2^{3} + 3^{3} - 4^{3} + . . . . . + 9^{3} = ?

Q. Find the sum of

1^{3} - 2^{3} + 3^{3} - 4^{3} + . . . . + 9^{3}

The sum of the series 1³ - 2³+ 3³- 4³+ ....... + 9³ is:

(1^{3} + 2^{3} + 3^{3} + 4^{3})^{- 3 / 2}

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13−23+33−43+....+93=

The correct option is A 42513−23+33−43+....+93=13+23+33+43+....+93−2(23+43+63+83)=(9×102)−16(13+23+33+43)=452−16(4×52)2=452−402=425

$1^{3} - 2^{3} + 3^{3} - 4^{3} + . . . . + 9^{3} =$

The correct option is A 425
$1^{3} - 2^{3} + 3^{3} - 4^{3} + . . . . + 9^{3} = 1^{3} + 2^{3} + 3^{3} + 4^{3} + . . . . + 9^{3} - 2 (2^{3} + 4^{3} + 6^{3} + 8^{3}) = (\frac{9 \times 10}{2}) - 16 (1^{3} + 2^{3} + 3^{3} + 4^{3}) = 45^{2} - 16 {(\frac{4 \times 5}{2})}^{2} = 45^{2} - 40^{2} = 425$