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`        Please solve the problem from binomial theorem.1)   Find the coefficient of x^65 in the expansion of x(x+1)^2(x+2)^3(x+3)^4.........(x+10)^112).  Find the coefficient of x^(n^2+n-14)/2 in the expansion of (x-1)(x^2-2)(x^3 -3).........(x^n-n)`
9 months ago

1670 Points
```							Roots of x(x+1)^2...(x+10)^11 are0, -1, -1, -2, -2, -2,..., -10, -10,...,-10Also, the degree of the above polynomial is 1+2+...+11= 66. So coefficient of x^65 is the following sum:∑r(r+1), r ranging from 0 to 10. This is because of viettas formulas taking the roots one at a time.The above sum is easy to find coz ∑r^2 and ∑r already have standard formulas
```
9 months ago
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• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions