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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.
The value of ` (n+ Rf ) "for x" = (1)/(sqrt(2)) ` is

A

7

B

8

C

9

D

10

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 `
Let ` f' = (sqrt( 2) - 1)^(7), 0 lt f' lt 1`
` therefore Rf' = (sqrt(2 + 1 )^(7) sqrt(2) - 1)^(7) = (1)^(7) = 1`
` therefore (n + Rf) = 7 + 1 = 8`
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