Question

Find the square of 2n +1 by 2n

Answer 1

Step-by-step explanation:

2n+1=k2

2n=k2−1=(k−1)(k+1)

n=(k−1)(k+1)2

LHS is always even so, RHS has to be even too.

So, either (k - 1) or (k + 1) has to be divisible by 2. In either case, k has to be a odd number for the above statement to hold true.

Thus, both (k - 1) and (k + 1) will be even.

So, lets say (k - 1) = 2a, then (k + 1) = 2a + 2

So, n=2a(2a+2)2=2a(a+1)

Now if a is odd then a+1 is even, and if a is even then a+1 is odd. In either case, we can get a factor of 2 out from them.

So, a(a+1)=2b

Answer 2

Answer:

hi

Answer is a(a+1)=2b

Step-by-step explanation:

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