Calculus Examples

$\sum_{n = 1}^{3} a_{n + 1} - a_{n}$

Step 1

Expand the series for each value of $n$ .

$a_{n + 1} - a_{n} + a_{n + 1} - a_{n} + a_{n + 1} - a_{n}$

Step 2

Substitute the values back and simplify $a_{n + 1} - a_{n} + a_{n + 1} - a_{n} + a_{n + 1} - a_{n}$ .

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Step 2.1

Add $a_{n + 1}$ and $a_{n + 1}$ .

$2 a_{n + 1} - a_{n} - a_{n} + a_{n + 1} - a_{n}$

Step 2.2

Add $2 a_{n + 1}$ and $a_{n + 1}$ .

$3 a_{n + 1} - a_{n} - a_{n} - a_{n}$

Step 2.3

Subtract $a_{n}$ from $- a_{n}$ .

$3 a_{n + 1} - 2 a_{n} - a_{n}$

Step 2.4

Subtract $a_{n}$ from $- 2 a_{n}$ .

$3 a_{n + 1} - 3 a_{n}$