Any shortcut?

Coefficient of $x^{49}$ in expansion of $(x+1)(x+2)(x+3)\dots(x+100)$

or you can generalise it for any power coefficient?

#Algebra

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
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Comments

me also waiting for this

Amrit Anand - 5 years, 8 months ago

then please share it again and again

Aman Rajput - 5 years, 7 months ago

@Calvin Lin sir ,,, will you please share this... i eagerly want to know this.... :/

Aman Rajput - 5 years, 8 months ago

Generalize? Yes, but the formula is too long and worth writing it down.

To solve this question, look at a similar question here.

Pi Han Goh - 4 years, 11 months ago

I already asked it on mathstack

Aman Rajput - 4 years, 11 months ago

I'm pessimistic that the formula will be helpful. It's like trying to remember all 4 quartic formulas.

Pi Han Goh - 4 years, 11 months ago

@Pi Han Goh – okay you can write the formula here

Aman Rajput - 4 years, 11 months ago

@Aman Rajput – Look at the solutions in the link that I've given. That's the general approach.

Pi Han Goh - 4 years, 11 months ago

Very simple . Use vietta's to generalise . Like : let f(x)= (x+1)(x+2)(x+3)......(x+n) then , f(x)= x^n + (1+2+3+...n).x^(n-1) + (1.2+1.3+1.4+...1.n+ 2.3+2.4+...2.n+3.4+3.5 +...).x^(n-2) +... I hope it is clear now!

Samanvay Vajpayee - 4 years, 9 months ago

so tell me the answer of the my question... i know that what you have written .

Aman Rajput - 4 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$