Consider the following predicate:\

P(n):,\\\\sum_(i=1)^n i=1+2+3+cdots+(n-1)+n=(n(n+1))/(2)

\ Answer the following questions about proving the above predicate for

n=1,2,3,4,cdots

using induction.\ Note: For this problem you get 5 submits.\ a. Select which of the following statements to prove for the base case.\ A.

P(k)=(k(k+1))/(2)

\ B.

P(1)=1

\ C.

(1+2+3+cdots+k

)

=

(

(k(k+1))/(2))->(1+2+3+cdots+(k+1)

)

=

(

((k+1)(k+2))/(2))

\ D.

1=(1(1+1))/(2)

\ E.

1+2+3+cdots+(k+1)=((k+1)(k+2))/(2)

\

F.1+2+3+cdots+k=(k(k+1))/(2)

\ b. Select which of the following statements to prove for the inductive step.\ A.

P(k)=(k(k+1))/(2)

\ B.

P(1)=1

\ C.

(1+2+3+cdots+k

)

=

(

(k(k+1))/(2))->(1+2+3+cdots+(k+1)

)

=

(

((k+1)(k+2))/(2))

Consider the following predicate: P(n):i=1ni=1+2+3++(n1)+n=2n(n+1) Answer the following questions about proving the above predicate for n=1,2,3,4, using induction. Note: Fr this problem you get 5 submits. a. Select which of the following statements to prove for the base case. A. P(k)=2k(k+1) B. P(1)=1 c. (1+2+3++k=2k(k+1))(1+2+3++(k+1)=2(k+1)(k+2)) D. 1=21(1+1) E. 1+2+3++(k+1)=2(k+1)(k+2) F. 1+2+3++k=2k(k+1) b. Select which of the following statements to prove for the inductive step. A. P(k)=2k(k+1) B. P(1)=1 c. (1+2+3++k=2k(k+1))(1+2+3++(k+1)=2(k+1)(k+2))