Use mathematical induction to prove the statement is true for all positive integers n.n ? 2n
What will be an ideal response?
| Sn: | n ? 2n |
| Step 2: | Assume Sk to be true, where k is a natural number, then |
Step 3: Find Sk+1.
Sk+1: k + 1 ? 2k+1
Step 4: Truth of Sk implies that Sk+1 is true.
k ? 2k This is Sk
2k ? 2*2k Mult both sides by 2
2k ? 2k+1 Adding exponents of right
k + k ? 2k+1 Substituting k + k for 2k
Since k is any natural number, 1 ? k,
then k + 1 ? k + k by adding k to both sides.
k + 1 ? 2k+1 Substituting k + 1 for k + k.
This is Sk+1.
Mathematics
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