`[1^3+2^3+3^3+…….+9^3+10^3]` is equal to

Options

A. a) 3575
B. b) 2525
C. c) 5075
D. d) 3025

Answer

To find the sum of the cubes of the first 10 natural numbers, we can use the formula for the sum of cubes:

\[ \text{Sum of cubes} = \left( \frac{n(n+1)}{2} \right)^2 \]

where \( n \) is the number of terms. In this case, \( n = 10 \).

### Step 1: Substitute \( n \) into the formula
We start by substituting \( n = 10 \) into the formula:

\[ \text{Sum of cubes} = \left( \frac{10(10+1)}{2} \right)^2 \]

### Step 2: Calculate \( n(n+1) \)
Next, we calculate \( n(n+1) \):

\[ 10(10+1) = 10 \times 11 = 110 \]

### Step 3: Divide by 2
Now, we divide this result by 2:

\[ \frac{110}{2} = 55 \]

### Step 4: Square the result
Finally, we square the result from the previous step:

\[ 55^2 = 3025 \]

### Final Answer
Thus, the sum of the cubes of the first 10 natural numbers is:

\[ \text{Sum} = 3025 \]

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