Questions: Find the indicated sum. Sum from k=1 to 64 of k Sum from k=1 to 64 of k= (Simplify your answer.)

Solution Steps

To find the indicated sum \(\sum_{k=1}^{64} k\), we can use the formula for the sum of the first \(n\) natural numbers, which is \(\frac{n(n+1)}{2}\). In this case, \(n = 64\).

To find the sum of the first \(64\) natural numbers, we use the formula: \[ \sum_{k=1}^{n} k = \frac{n(n+1)}{2} \] Substituting \(n = 64\): \[ \sum_{k=1}^{64} k = \frac{64(64 + 1)}{2} = \frac{64 \times 65}{2} \]

Calculating the product: \[ 64 \times 65 = 4160 \] Now, divide by \(2\): \[ \frac{4160}{2} = 2080 \]

Final Answer