Multiple choices 11/50
(Choose 1 answer)
A. (iii)
B. (iv)
C. (i)
D. (ii)
Next
E. None of the other choices is correct.
Prove that P(n)="1.1!+2.2!+3.3!+...+n.n!=(n+1)!-1~for~all~n\ge1^{"}is true.
In the Principle of Mathematical Induction, assuming that P(k) is true for some k, in order to prove P(k+1)i true we should
(i) use P(k)="1.1!+2.2!+3.3!+...+k.k!=(k+1)!-1" is true.
(ii) use P(k-1)="1.1!+2.2!+3.3!+...+(k-1).(k-1)!=k!-1^{"}is
true.
(iii) P(k-2)=^{*}1.1!+2.2!+3.3!+...+(k-2).(k-2)!=(k-1)!-1^{*} is true.
(iv) use P(k+1)=^{\leftrightarrow}1.1!+2.2!+3.3!+...+(k+1).(k+1)!=(k+2)!-1^{"} is true.
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