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cofficient of xpower8 in x-1* x-2*.............x-10 is method

cofficient of xpower8 in x-1* x-2*.............x-10 is method
 

Grade:12th pass

2 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
8 years ago
Question is not clear. Please repost and write in proper language.
jagdish singh singh
173 Points
8 years ago
\hspace{-0.6 cm}$ Here we have to find Coeff. of $x^8$ in $(x-1)(x-2)......(x-9)(x-10)$\\\\\\So $x^8$ in $x^{10}-x^9\sum^{10}_{i=1}i+x^8\mathop{\sum\sum}_{0\leq i<j\leq 10}i\cdot j-.......$\\\\\\So $\mathop{\sum\sum}_{0\leq i<j\leq 10}i\cdot j=\frac{1}{2}\left[\left(\sum^{10}_{r=1}i\right)^2-\sum^{10}_{i=1}i^2\right] = (55)^2-55\cdot 7=55\cdot 48$

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