Answer:
Step-by-step explanation:
Mathematical induction involves the following steps:
1) An arbitrary or a constrained value test.
2)testing it for a general number k
3)proving it for k+1
so lets try your question.
It says that prove the formula for n=1
simply put n=1 in the formula and see if it is true.
3^n>n^2
3^1>1^2
3>1 (It's true for n=1)
clearly 3 is bigger than 1 so n=1 is true
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now testing it for n=k
3^k>k^1
3^k>k......(1)
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now proving it for n=K+1
3^k+1>k+1
3*3^k>k+1
we know from (1) that 3^k>k
so then 3*(k+1)>k+1 (proved) replacing 3^k with K+1 because as stated above it is bigger than k so it becomes (k+1)
Now 3 multiply by (k+1) is bigger than K+1 itself this proves that the formula is true.
Note:
I don't know how much your teacher has demanded from you but if it is only for n=1 then you can skip the rest of the question.
