Maths
posted by Natasha .
The second term in the expansion of (1x)(1+2x)Λn is 19x. Find the value of n

(1+2x)^n = 1 + n(2x) + n(n1)/2! (2x) + n(n1)(n2)/3! (2x)^3 + ....
so (1x)(1+2x)^2
= (1x)(1 + n(2x) + n(n1)/2! (2x)^2 + n(n1)(n2)/3! (2x)^3 + ....)
= 1 + 2nx + 4n(n1)/2 x^2 + 8n(n1)(n2)/6 x^3 + ...  x  2nx^2  4n(n1)/2 x^3  ..
so the only two terms with a first degree x term are
2nx  x
the 2nx  x = 19
2n  1 = 19
2n = 20
n = 10
Respond to this Question
Similar Questions

Maths
The 3rd term of an AP is 10 more than the first term while the fifth term is 15 more than the second term.find the sum of the 8th and 15 term of AP.if the 7th term is seven times the first term. 
maths
find the first 3 terms in the expansion of (x+4)(1+3x)^2 as a series in ascending powers. I expanded the second bracket using binomial expansion and got 1 6x +27x^2 108x^3 how do I combine (x+4) with the expansion? 
maths
Obtain the binomial expansion of (2x) (1+1/2x)^8 in ascending powers of x as far as the term in x^3. Use your result to estimate the value of 1.9 times (1.05)^8. 
maths
given that x+1/x=3 (a) expand (x+1/x)^3 and use your expansion to show that x^3+1/x^3=18. (ii) expand (x+1/x)^5, using your expansion and the previous results to find the value of x^5+1/x^5 
maths
in the binomial expansion of (1+x/k)^n, where k is a constant and n is a positive integer, the coefficients of x and x^2 are equal. (a) show that 2k=n1 (b) deduce the value of k. Hence find the 1st 3 terms in the expansion in ascending … 
maths
in an AP the third term is equal to five times the sixth term. the second term is lesser by 3 than twice the fourth term. find the term of AP 
maths
find term independent of y in expansion of,[x^4÷y^3+y^2÷2x]^10 
maths
The fifth term of an arithmetic sequence is 23 and 12th term is 72. And they say 1. Determine the first three terms of the sequences and the nth term. 2. What is the value of the 10th term. 3. Which term has a value of 268. 
maths science and geography
in a geometric sequence,the fifth term is four times the third term,and the second term is 4.if r<0 determine the value of r,the common ratio 
maths binomial expansion
find five term of the expansion (x+y/2)^1/3 show step plz