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Magical Mathematics[Interesting Approach]> Find the co-efficient of x^19 in the foll...

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Find the co-efficient of x^19 in the following expression: (x+1)(x+2)(x+3).....(x+400) please give the solution

Shrey , 10 Years ago

Grade 11

2 Answers

Shrey

Last Activity: 10 Years ago

Please reply fast

Arun Kumar

Last Activity: 10 Years ago

This is equation of degree 400

$C(x^{400})=1;\\ C(x^{400-1})=\sum_{i_{1},i_{2}=1,i_{1}\neq i_{2}}^{400}i_{1}*i_{2};\\ C(x^{400-2})=\sum_{i_{1},i_{2}=1,i_{3}=1,i_{1}\neq i_{2}\neq i_{3}}^{400}i_{1}*i_{2}*i_{3};\\ ......\\ C(x^{400-381})=\sum_{i_{1},i_{2}=1,i_{3}=1...,i_{382}=1,i_{1}\neq i_{2}\neq i_{3}...\neq i_{382}}^{400}i_{1}*i_{2}*i_{3}....*i_{382};\\$

This is all we can do here. Calculation part won't be asked.

Arun Kumar

IIT Delhi

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