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If a=min (x^2 +4x+5, x in R) and b= lim(...

If `a=min (x^2 +4x+5, x in R)` and `b= lim_(theta->0)(1-cos2theta)/theta^2` then the value of `sum_(r=0)^n a^rb^(n-r)` is

A

`3^(n)`

B

`4^(n)`

C

`5^(n)`

D

`6^(n)`

Text Solution

Verified by Experts

`(4x^(2)+1)^(n)=underset(r=0)overset(n)suma_(r)(1+x^(2))^(n-r)x^(2r)`
`rArr (1+(3x^(2))/(1+x^(2)))^(n)=underset(r=0)overset(n)suma_(r)((x^(2))/(1+x^(2)))^(r)`
`:. a_(r) = .^(n)C_(r)3^(r)`
`:. underset(r=0)overset(n)suma_(r) = underset(r=0)overset(n)sum.^(n)C_(r)3^(r)=(1+3)^(n)=4^(n)`
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