Just need C done please :) Below are references for working the problem P. so me
ID: 1721299 • Letter: J
Question
Just need C done please :)
Below are references for working the problem
P. so me s(6) true or some positive integer K 1.c., K = K ): y adding 1 to each side of this equality, we obtain the equality k + 1 2, d so S(k + 1) is true. , From this inductive step, some might be tempted to conclude that S(n) is true r each positive integer n, but, in fact, this statement is not true for any positive teger n. Hence, to avoid reaching such absurd conclusions through mathematical duction, it is imperative to verify both steps in the induction process. 1.8 Prove the following statements using the Principle of Mathematical Induction: a. For each positive integer n, 1+ 3 + 5 + + (2n-1)=nv b. For each positive integer n, 12 2232 n21) c. For each positive integer n,3 3 3 +33Explanation / Answer
3 = (9-3)/2
=>
the statement is true for n = 1
let the statement be true for n = k, i.e
3 + 3^2 + ...+3^k = (3^(k+1) -3)/2
=>
3 + 3^2 + ...+3^k + 3^(k+1)= (3^(k+1) -3)/2 + 3^(k+1)
=>
3 + 3^2 + ...+3^k + 3^(k+1)= [3^(k+1) -3 + 2*3^(k+1)]/2
=>
3 + 3^2 + ...+3^k + 3^(k+1)= [3*3^(k+1) -3 ]/2
=>
3 + 3^2 + ...+3^k + 3^(k+1)= [3^(k+2) -3 ]/2
=>
the statement is true is for n = k+1
thus proved by induction
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