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What-is-the-sum-of-the-coefficients-in-the-expansion-of-2015v-2015u-1-2015-




Question Number 111393 by Aina Samuel Temidayo last updated on 03/Sep/20
What is the sum of the coefficients in the  expansion of (2015vāˆ’2015u+1)^(2015) ?
$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{coefficients}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{2015v}āˆ’\mathrm{2015u}+\mathrm{1}\right)^{\mathrm{2015}} ? \\ $$
Commented by mr W last updated on 03/Sep/20
1
$$\mathrm{1} \\ $$
Commented by Aina Samuel Temidayo last updated on 03/Sep/20
Solution please?
$$\mathrm{Solution}\:\mathrm{please}? \\ $$
Commented by PRITHWISH SEN 2 last updated on 03/Sep/20
put v=u=1
$$\mathrm{put}\:\mathrm{v}=\mathrm{u}=\mathrm{1} \\ $$
Commented by Aina Samuel Temidayo last updated on 03/Sep/20
Why?
$$\mathrm{Why}? \\ $$
Commented by PRITHWISH SEN 2 last updated on 03/Sep/20
if you put v=u=1 then the v and u will vanish  from the expansion and only the coefficients  will remain.
$$\mathrm{if}\:\mathrm{you}\:\mathrm{put}\:\mathrm{v}=\mathrm{u}=\mathrm{1}\:\mathrm{then}\:\mathrm{the}\:\mathrm{v}\:\mathrm{and}\:\mathrm{u}\:\mathrm{will}\:\mathrm{vanish} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{and}\:\mathrm{only}\:\mathrm{the}\:\mathrm{coefficients} \\ $$$$\mathrm{will}\:\mathrm{remain}.\: \\ $$
Commented by Aina Samuel Temidayo last updated on 03/Sep/20
Oh. Cool. Thanks.
$$\mathrm{Oh}.\:\mathrm{Cool}.\:\mathrm{Thanks}. \\ $$

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