Satvik's Sum
If we expand the polynomial ( 3 x − 1 ) 9 , it takes the form
a x 9 + b x 8 + c x 7 + d x 6 + e x 5 + f x 4 + g x 3 + h x 2 + i x + j
then what is the value of a + b + c + d + e + f + g + h + i ?
The answer is 513.
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1 solution
Nice approach, Arijit, many people are tempted to use the binomial theorem.
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i think in the expansion - using binomial expansion , the power of first term decreases(as you have shown) and the 2nd term increases . Thus for odd powers of -1 , instead of + sign it should be minus(for eg the third term would have odd power of -1 , so instead of + it should be - , if not so , then we have to do it with regular binomial expansion) @Satvik Golechha , correct me if i am wrong.
Thanks !
Wow! Never thought of that, I just used brute force binomial expansion. Very nice solution!
Does this approach always work if you want to calculate the sum of coefficients? If yes, why does it work?
Perfect. upvoted .
Same as I did! :)
to get the sum of the coefficients put x=1 and we get 512 .But here ' j ' is not included so we'll have to add +1 to 512 because the last term of this expansion is 9C9(-1)^9 = -1 . hence answer is 513 .