Q. 124.2( 5 Votes )

# If the coefficients of (r – 5)th and (2r – 1)th terms in the expansion of (1 + x)^{34} are equal, find the value of r.

Answer :

To find: the value of r with respect to the binomial expansion of (1 + x)^{34} where the coefficients of the (r – 5)th and (2r – 1)th terms are equal to each other

Formula Used:

The general term, T_{r+1} of binomial expansionis given by,

T_{r+1} ^{n}C_{r} x^{n-r} y^{r} where

^{n}C_{r}

Now, finding the (r – 5)th term, we get

T_{r-5}^{34}C_{r-6}

Thus, the coefficient of (r – 5)th term is ^{34}C_{r-6}

Now, finding the (2r – 1)th term, we get

T_{2r-1}^{34}C_{2r-2}

Thus, coefficient of (2r – 1)th term is ^{34}C_{2r-2}

As the coefficients are equal, we get

^{34}C_{2r-2}^{34}C_{r-6}

2r-2=r-6

r=-4

Value of r=-4 is not possible

2r-2+r-6=34

3r=42

r=14

Thus, value of r is 14

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