Question

How many consecutive odd numbers must be added to get the sum equal to 24 Cube? *i​

Answer 1

Answer:

This is the answer for the following question

Answer 2

Answer:

Therefore, consecutive odd numbers must be added to get the sum equal to $24^{3}$= 553 + 555 + -------------- + 597 + 599.

⇒ 13824 = $24^{3}$.

Step-by-step explanation:

We know,

1 = $1^{3}$

3 + 5 = 8 = $2^{3}$

7 + 9 + 11 = 27 = $3^{3}$

13 + 15 + 17 + 19 = 64 = $4^{3}$

21 + 23 + 25 + 27 + 29 = 125 = $5^{3}$

Following this pattern we will find the number of odd numbers which add the sum of $24^{3}$.

$n^{2} - n + 1 \\24^{2} - 24 + 1\\ 576 - 23\\553$

∴ 553 + 555 + -------------- + 597 + 599

⇒ 13824 = $24^{3}$.

So, consecutive odd numbers must be added to get the sum equal to $24^{3}$= 553 + 555 + -------------- + 597 + 599.

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