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Patterns in Whole Numbers

Find the valu...

Question

Find the value of 13 + 23 + 33 +…+ 93, using the following pattern.

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Solution

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Q. Observe the following pattern:
1³ = 1
1³ + 2³ = (1 + 2)²
1³ + 2³ + 3³ = (1 + 2 + 3)²
Write the next three rows and calculate the value of 1³ + 2³+ 3³ + ... + 9³+ 10³ by the above pattern.

Q. The value of

\frac{1^{3} + 2^{3} + 3^{3} +______+ 10^{3}}{1 + 2 + 3 +______+ 10}

______________.

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

1^{3} + 2^{3} + 3^{3} + . . . . . + 9^{3} = 2025

, find the value close to

(0.11)^{3} + (0.22)^{3} + . . . . . + (0.99)^{3}

Q. Find the sum of

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

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