Let P(k) be a statement that 11⋅2+12⋅3+…+1k⋅(k+1)= for: The basis step to prove P(k) is that at k = 1, _____ is true. for:Show that P(1) is true by completing the basis step proof. Left side of P(k) and Right side of P(k) for: Identify the inductive hypothesis used to prove P(k). for: Identify the inductive step used to prove P(k+1).

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Let P(k) be a statement that 11⋅2+12⋅3+…+1k⋅(k+1)=  for: The basis step to prove P(k) is that at k = 1, _____ is true.  for:Show that P(1) is true by completing the basis step proof. Left side of P(k) and Right side of P(k)  for: Identify the inductive hypothesis used to prove P(k).  for: Identify the inductive step used to prove P(k+1).

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Let the property P(k) be 11⋅2+12⋅3+13⋅4+…+1k(k+1)=kk+1  Show that P(k) is true for all integers k≥1 using mathematical induction  Basis Step: P(k) is true:  That is to show that 11⋅2=11+1  The left hand side of the equation is 11⋅2=12 and right-hand side is  11+1=12  It follows that 12=12  Hence P(1) is true.  Show that for all integers n≥1, P(k) is true then P(k+1) is also true:  Suppose P(k) is true.  Then the inductive hypothesis is  11⋅2+12⋅3+13⋅4+…+1k(k+1)  Now show that P(k+1) is true.  That is to show that  11⋅2+12⋅3+13⋅4+…+1k(k+1)+1(k+1)(k+2)=k+1(k+1)+1  Or, equivalently that  11⋅2+12⋅3+13⋅4+…+1(k+1)(k+2)=k+1k+2  The left-hand side of P(k+1) is  11⋅2+12⋅3+13⋅4+…+1k(k+1)+1(k+1)(k+2)  =kk+1+1(k+1)(k+2)  =1k+1(k+1k+2)  =1k+1(k2+2k+1k+2)  =1k+1((k+1)2k+2)

Let P(k) be a statement that \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}

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