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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 kth term is having greatest coefficient , the sum of all possible value of k, is

A

7

B

9

C

11

D

13

Text Solution

Verified by Experts

The correct Answer is:
b
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 , n= 7
` therefore ` Greatest coefficient = ` (""^(7)C_(7-1))/(2) " or " ""^(7)C_(3)`
Sum of values of k = (3 + 1) + (4 + 1) = 9 `
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