If the number of integral terms in the expans | vedclass

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Question

$T _{ r +1}={ }^{ n } C _{ r }(3)^{\frac{ n - r }{2}}(5)^{\frac{ r }{8}} \quad( n \geq r )$

Clearly r should be a multiple of 8 .

$\because$ the

Vedclass · Accepted Answer

$256$

Vedclass · Answer

$T _{ r +1}={ }^{ n } C _{ r }(3)^{\frac{ n - r }{2}}(5)^{\frac{ r }{8}} \quad( n \geq r )$

Clearly r should be a multiple of 8 .

$\because$ there are exactly 33 integral terms

Possible values of $r$ can be

$0,8,16, \ldots \ldots \ldots, 32 	imes 8$

$	herefore$ least value of $n =256$

If the number of integral terms in the expansion of $\left(3^{\frac{1}{2}}+5^{\frac{1}{8}}\right)^{\text {n }}$ is exactly $33,$ then the least value of $n$ is

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