Question

Prove that /( − 1) + /( + 1) = 2
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Answer 1

Answer:

Let n=1,

1⋅1!=1⋅1=1=(n+1)!−1=2!−1=2−1=1

Induction Step:

Assume f(k)=1⋅1!+2⋅2!+⋯+k⋅k!=(k+1)!−1

F(k+1)=1⋅1!+2⋅2!+⋯+k⋅k!+(k+1)⋅(k+1)!=(k+1)! −1+(k+1)⋅(k+1)!=(k+1)!⋅((k+1)−1)=(k+1)!⋅(k)

I think I'm supposed to make (k+1)!⋅k=((k+1)+1)!+1=(k+2)!−1 but I'm

Step-by-step explanation:

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