What is (k+1)!-1+(k+1)(k+1)! ?

The solution to (k+1)!-1+(k+1)(k+1)! is k(k+1)!+2(k+1)!-1

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simplify (k+1)!-1+(k+1)(k+1)!

simplify

(k + 1)! - 1 + (k + 1) (k + 1)!

k (k + 1)! + 2 (k + 1)! - 1

Solution steps

(k + 1)! - 1 + (k + 1) (k + 1)!

= (k + 1)! - 1 + (k + 1)! (k + 1)

Expand

(k + 1)! (k + 1) : k (k + 1)! + (k + 1)!

= (k + 1)! - 1 + k (k + 1)! + (k + 1)!

Simplify

(k + 1)! - 1 + k (k + 1)! + (k + 1)! : k (k + 1)! + 2 (k + 1)! - 1

= k (k + 1)! + 2 (k + 1)! - 1

(4 + 2 i) + (- 12 - 2 i)

- 3 \cdot (- 4)

(x + 4) (x^{2} - 4 x + 16)

(2 x^{2} + 3)^{2}

2^{2 + 1}

What is (k+1)!-1+(k+1)(k+1)! ?
The solution to (k+1)!-1+(k+1)(k+1)! is k(k+1)!+2(k+1)!-1