The following are lines from a proof by induction. Which line uses the inductive hypothesis? Statement: For every positive integer n ,
1+2+ \dots + n = \frac{n(n+1)}{2} Proof. Since 1=(1\cdot 2)/2 , the statement is true for n=1 . Assume the statement is true for a positive integer k . 1+2+\dots+k+(k+1) = k(k+1)/2 +(k+1) Now k(k+1)/2+(k+1) = (k+1)(k/2 + 1) = (k+1)(k+2)/2 By the principle of mathematical induction, 1+2+\dots+n = n(n+1)/2 for every positive integer n .

Question

The following are lines from a proof by induction. Which line uses the inductive hypothesis? Statement: For every positive integer   n ,  
   1+2+ \dots + n = \frac{n(n+1)}{2}  Proof.  Since   1=(1\cdot 2)/2 , the statement is true for   n=1 . Assume the statement is true for a positive integer   k .  1+2+\dots+k+(k+1) = k(k+1)/2 +(k+1)  Now   k(k+1)/2+(k+1) = (k+1)(k/2 + 1) = (k+1)(k+2)/2  By the principle of mathematical induction,   1+2+\dots+n = n(n+1)/2  for every positive integer   n .

Answer

The inductive hypothesis is used in step 4.

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The inductive hypothesis is used in step 3.

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The inductive hypothesis is used in step 1.

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The inductive hypothesis is used in step 2.

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The inductive hypothesis is used in step 5.

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The following are lines from a proof by induction. Which line uses the inductive...

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