If `y=1^(3)+2^(3)+3^(3)+4^(3)+5^(3)+6^(3)`, then find the value of `y-1`.

Options

A. 429
B. 439
C. 440
D. 441

Answer

To solve the problem, we need to calculate the value of \( y \) given by the expression:

\[ y = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 \]

### Step 1: Calculate each term in the expression

1. Calculate \( 1^3 \):
\[ 1^3 = 1 \]

2. Calculate \( 2^3 \):
\[ 2^3 = 8 \]

3. Calculate \( 3^3 \):
\[ 3^3 = 27 \]

4. Calculate \( 4^3 \):
\[ 4^3 = 64 \]

5. Calculate \( 5^3 \):
\[ 5^3 = 125 \]

6. Calculate \( 6^3 \):
\[ 6^3 = 216 \]

### Step 2: Add all the calculated values

Now, we will add all the values calculated in Step 1:

\[ y = 1 + 8 + 27 + 64 + 125 + 216 \]

Calculating this step by step:

- \( 1 + 8 = 9 \)
- \( 9 + 27 = 36 \)
- \( 36 + 64 = 100 \)
- \( 100 + 125 = 225 \)
- \( 225 + 216 = 441 \)

Thus, we find:

\[ y = 441 \]

### Step 3: Calculate \( y - 1 \)

Now we need to find \( y - 1 \):

\[ y - 1 = 441 - 1 = 440 \]

### Final Answer

The value of \( y - 1 \) is:

\[ \boxed{440} \]