Calculus Examples

$\sum_{k = 1}^{5} k (6 k + 7)$

Step 1

Simplify the summation.

Tap for more steps...

Step 1.1

Apply the distributive property.

$k (6 k) + k \cdot 7$

Step 1.2

Rewrite using the commutative property of multiplication.

$6 k \cdot k + k \cdot 7$

Step 1.3

Move $7$ to the left of $k$ .

$6 k \cdot k + 7 \cdot k$

Step 1.4

Multiply $k$ by $k$ by adding the exponents.

Tap for more steps...

Step 1.4.1

Move $k$ .

$6 (k \cdot k) + 7 \cdot k$

Step 1.4.2

Multiply $k$ by $k$ .

$6 k^{2} + 7 \cdot k$

$6 k^{2} + 7 k$

Step 1.5

Rewrite the summation.

$\sum_{k = 1}^{5} 6 k^{2} + 7 k$

Step 2

Expand the series for each value of $k$ .

$6 \cdot 1^{2} + 7 \cdot 1 + 6 \cdot 2^{2} + 7 \cdot 2 + 6 \cdot 3^{2} + 7 \cdot 3 + \dots + 6 \cdot 5^{2} + 7 \cdot 5$

Step 3

Simplify the expanded form.

$435$