What is the sum of the series 1^3 - 2^3 + 3^3 | vedclass

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(C) The given series is $S = 1^3 - 2^3 + 3^3 - 4^3 + 5^3 - 6^3 + 7^3 - 8^3 + 9^3$. We can group the terms as follows: $S = (1^3) + (3^3 - 2^3) + (5^3

Vedclass · Accepted Answer

$425$

Vedclass · Answer

(C) The given series is $S = 1^3 - 2^3 + 3^3 - 4^3 + 5^3 - 6^3 + 7^3 - 8^3 + 9^3$. We can group the terms as follows: $S = (1^3) + (3^3 - 2^3) + (5^3 - 4^3) + (7^3 - 6^3) + (9^3 - 8^3)$. Using the identity $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$,where $a - b = 1$: $S = 1 + (3^2 + 3 	imes 2 + 2^2) + (5^2 + 5 	imes 4 + 4^2) + (7^2 + 7 	imes 6 + 6^2) + (9^2 + 9 	imes 8 + 8^2)$. $S = 1 + (9 + 6 + 4) + (25 + 20 + 16) + (49 + 42 + 36) + (81 + 72 + 64)$. $S = 1 + 19 + 61 + 127 + 217$. $S = 425$.

What is the sum of the series $1^3 - 2^3 + 3^3 - 4^3 + 5^3 - 6^3 + 7^3 - 8^3 + 9^3$?

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