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Consider the binomial expansion of R = ...

Consider the binomial expansion of ` R = (1 + 2x )^(n) = I + f ` , where I
is the integral part of R and f is the fractional part of R , n `in` N .
Also , the sum of coefficient of R is 2187.
If ith term is the geratest term for x= 1/3, then i equal

A

4

B

5

C

6

D

7

Text Solution

Verified by Experts

The correct Answer is:
a
Here , ` (1 + 2)^(n) = 2187`
` 3^(n) = 2187 = 3^(7) rArr n = 7`
At ` x = (1)/(sqrt(2)) , R = (sqrt(2) + 1)^(7) = I + f `
Here , `m= |((n +1)(x))/(1 + x)| `
` = | ((7+1)(2xx(1)/(3)))/(1 + 2 xx(1)/(3))| = - (8xx(2)/(3))/((5)/(3)) = (16)/(5) = 3.2`
` T_([m]+1) = T_(3+1) = T_(4)`
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