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As we know that the  term   in the binomial expansion of    is given by  Now let's assume  happens in the  term of the binomial expansion of  So, On comparing the indices of x we get, Hence the coefficient of the   in  is 
As we know from Binomial Theorem, Here putting a = 3, we get,  Hence Proved.
If we want to prove that  is divisible by 64, then we have to prove that   As we know, from binomial theorem,  Here putting x = 8 and replacing m by n+1, we get, Now, Using This, Hence is divisible by 64.
Using Binomial Theorem, the expressions  and  can be expressed as , From Here, Now, Using this, we get 
Using Binomial Theorem, the expressions  and  can be expressed as From Here, Now, Using this, we get 

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P Pankaj Sanodiya
As we can write 102 in the form 100+2

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P Pankaj Sanodiya
Given, The Expression:    the expansion of this Expression is,

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P Pankaj Sanodiya
Given, The Expression:    the expansion of this Expression is,

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P Pankaj Sanodiya
Given, The Expression:    the expansion of this Expression is,

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P Pankaj Sanodiya
Given, The Expression:    the expansion of this Expression is,

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P Pankaj Sanodiya
Given, The Expression:    the expansion of this Expression is,
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