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Mathematical Induction:-
- We are given statement to prove by the Principle of Mathematical Induction.
- The
term isn't given. We must figure it out.
- Each term has sum of cubes in numerator and sum of odd numbers in the denominator.
- Observing the pattern, the
term must contain sum of cubes of n terms in the numerator and sum of first n odd numbers in the denominator.
- While proving, we would be using two results:
The second result above is a simple A.P. with first time 1, common difference 2, and total n terms. So sum can be found easily and it is obtained as .
Let us name the statement as P(n). So, we have to prove:
Checking for P(1):
Hence, P(1) is true.
Suppose P(k) is true. Then:
We now need to prove for P(k+1).
To Prove:-
Consider the LHS:-
Thus, P(k+1) is true provided P(k) is true.
Now, P(1) is true and P(k) is true P(k+1) is true.
So, P(n) is true for all 
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