Question

Find the coefficient of x^5
in the expansion of 1+(1+x) +
(1+x)2+ +(1+x)“ 10.​

Answer 1

Answer:

(i) x10 in the expansion of (2x2 – 1/x)20 Given as (2x2 – 1/x)20 If x10 occurs in the (r + 1)th term in the given expression. Now, we have: Tr+1 = nCr xn-r ar (ii) x7 in the expansion of (x – 1/x2)40 Given as (x – 1/x2)40 If x7 occurs at the (r + 1)th term in the given expression. Now, we have: Tr+1 = nCr xn-r ar (iii) x-15 in the expansion of (3x2 – a/3x3)10 Given as (3x2 – a/3x3)10 If x−15 occurs at the (r + 1)th term in the given expression. Now, we have: Tr+1 = nCr xn-r ar (iv) x9 in the expansion of (x2 – 1/3x)9 Given as (x2 – 1/3x)9 If x9 occurs at the (r + 1)th term in the above expression. Now, we have: Tr+1 = nCr xn-r ar For this term to contain x9, we must have: 18 − 3r = 9 3r = 18 – 9 3r = 9 r = 9/3 = 3 Read more on Sarthaks.com - https://www.sarthaks.com/801963/find-the-coefficient-of-i-x-10-in-the-expansion-of-2x-2-1-x-20-ii-x-7-in-the-expansion-of-x-1-x-2-40?show=801987#a801987

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