Use mathematical induction to prove the formula for all integers n>_1. 2+4+6+8+...+2n=n(n+1) Find S1 = ? Assume that Sk=2+4+6+8+...+2k=k(k+1). Then Sk+1= Sk+ak+1=(2+4+6+8+...+2k)+ak+1 ak+1=? Use the equation for ak+1 and Sk to find the equation for Sk+1. Sk+1= ?
Use mathematical induction to prove the formula for all integers n>_1. 2+4+6+8+...+2n=n(n+1) Find S1 = ? Assume that Sk=2+4+6+8+...+2k=k(k+1). Then Sk+1= Sk+ak+1=(2+4+6+8+...+2k)+ak+1 ak+1=? Use the equation for ak+1 and Sk to find the equation for Sk+1. Sk+1= ?
Chapter8: Sequences, Series,and Probability
Section8.4: Mathematical Induction
Problem 3ECP
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Use mathematical induction to prove the formula for all integers n>_1.
2+4+6+8+...+2n=n(n+1)
Find S1 = ?
Assume that Sk=2+4+6+8+...+2k=k(k+1).
Then Sk+1= Sk+ak+1=(2+4+6+8+...+2k)+ak+1
ak+1=?
Use the equation for ak+1 and Sk to find the equation for Sk+1.
Sk+1= ?
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