what-the-cooefficient-of-x-10-from-1-x-1-2x-2-1-3x-3-1-2020x-2020-

Question Number 115742 by bemath last updated on 28/Sep/20

w h a t t h e c o o e f f i c i e n t o f x^{10} f r o m

(1 + x) \times (1 + 2 x^{2}) \times (1 + 3 x^{3}) \times \dots \times (1 + 2020 x^{2020})

Answered by mr W last updated on 28/Sep/20

x^{10} : 10 = 10

x^{9 + 1}, x^{8 + 2}, x^{7 + 3}, x^{6 + 4} : 9 \times 1 + 8 \times 2 + 7 \times 3 + 6 \times 4 = 70

x^{7 + 2 + 1}, x^{6 + 3 + 1}, x^{5 + 4 + 1}, x^{5 + 3 + 2} : 7 \times 2 \times 1 + 6 \times 3 \times 1 + 5 \times 4 \times 1 + 5 \times 3 \times 2 = 82

x^{4 + 3 + 2 + 1} : 4 \times 3 \times 2 \times 1 = 24

Σ = 10 + 95 + 72 + 24 = 186

\Rightarrow c o e f . o f x^{10} i s 186 .

Commented by mr W last updated on 28/Sep/20

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