Q.

The mean of the coefficients of x,  x2,....,x7 in the binomial expansion of (2+x)9 is _______

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answer is 2736.

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Detailed Solution

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E(2+x)9
=9c029x0+9c128x1+9c227x2+9c326x3+9c425x4+9c524x5+9c623x6 +9c722x7+9c821x8+9c920x9
The mean of the coefficients of x,  x2,....,x7 in the binomial expansion of (2+x)9  is
9c029+9c128+9c227+9c326+9c425+9c524+9c623 +9c722+9c821+9c9209c0299c821-9c9207
=39299(2)17   (    (x+1)9  at   x=2)    =191527  =2736

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