1.

If (1+x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + "….." + C_(n)x^(n), then C_(0) - (C_(0) + C_(1)) +(C_(0) + C_(1) + C_(2)) - (C_(0) + C_(1) + C_(2) + C_(3))+"….."(-1)^(n-1) (C_(0) + C_(1) + "……" + C_(n-1)) is (where n is even integer and C_(r) = .^(n)C_(r))

Answer» <html><body><p>a positive value<br/>a negative value<br/>divisible by `<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>^(n-1)`<br/>divisible by `2^(n)`</p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :For `n = 2m`, the given expression is <br/> `C_(<a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a>)-(C_(0)+C_(1))+(C_(0)+C_(1)+C_(2))-(C_(0)+C_(1)+C_(2)+C_(3))+"....."(-1)^(n-1)(C_(0)+C_(1)+"....."+C_(n-1))` <br/> `= C_(0)-(C_(0)+C_(1))+(C_(0)+C_(1)+C_(2))-(C_(0)+C_(1)+C_(2)+C_(3))+"....."-(C_(0)+C_(1)+"...."+C_(2m-1))` <br/> `= - (C_(1)+C_(3)+C_(<a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>)+"...."+C_(2m-1))` <br/> `= - (C_(1)+C_(3)+C_(5)+"......."+C_(n-1)) = -2^(n-1)`</body></html>


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