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Please solve this question relates to binomial......

Please solve this question relates to binomial......

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Grade:12

1 Answers

Aditya Gupta
2081 Points
5 years ago
although this ques looks difficult, but is EXTREMELY simple.
put x= – 1/(1+loge10^n)
so the term becomes
nCr*x^r*(1+rloge10)= nCr*x^r + r*nCr*x^r*loge10
obviously the sum of nCr*x^r is known by BT to be (1+x)^n
now sum of r*nCr*x^r*loge10 can be found out by replacing r*nCr by n*(n-1)C(r-1), so sum will be loge10*n*(1+x)^(n-1)
after all this, simplify both the individual sums and add them to get zero. note that you can also do this by differentiation. however my solution is without using calculus
 

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