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Question-187235




Question Number 187235 by Rupesh123 last updated on 15/Feb/23
Commented by MJS_new last updated on 15/Feb/23
I believe it′s 3
$$\mathrm{I}\:\mathrm{believe}\:\mathrm{it}'\mathrm{s}\:\mathrm{3} \\ $$
Commented by Rasheed.Sindhi last updated on 16/Feb/23
What′s the base of  your belief sir?
$${What}'{s}\:{the}\:{base}\:{of}\:\:{your}\:{belief}\:\boldsymbol{{sir}}? \\ $$
Commented by MJS_new last updated on 17/Feb/23
the sequence of the last digits of ⌊(1+(√2))^n ⌋  beginning with n=0 is:  1 2 5 4 3 2 7 8 3 6 5 8 1 2 5 4 3 2 7 and now my  calculator is getting inaccurate but it looks  good...
$$\mathrm{the}\:\mathrm{sequence}\:\mathrm{of}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digits}\:\mathrm{of}\:\lfloor\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)^{{n}} \rfloor \\ $$$$\mathrm{beginning}\:\mathrm{with}\:{n}=\mathrm{0}\:\mathrm{is}: \\ $$$$\mathrm{1}\:\mathrm{2}\:\mathrm{5}\:\mathrm{4}\:\mathrm{3}\:\mathrm{2}\:\mathrm{7}\:\mathrm{8}\:\mathrm{3}\:\mathrm{6}\:\mathrm{5}\:\mathrm{8}\:\mathrm{1}\:\mathrm{2}\:\mathrm{5}\:\mathrm{4}\:\mathrm{3}\:\mathrm{2}\:\mathrm{7}\:\mathrm{and}\:\mathrm{now}\:\mathrm{my} \\ $$$$\mathrm{calculator}\:\mathrm{is}\:\mathrm{getting}\:\mathrm{inaccurate}\:\mathrm{but}\:\mathrm{it}\:\mathrm{looks} \\ $$$$\mathrm{good}… \\ $$
Commented by Rasheed.Sindhi last updated on 17/Feb/23
Thanks a lot sir!
$$\boldsymbol{\mathcal{T}{hanks}}\:\boldsymbol{{a}}\:\boldsymbol{{lot}}\:\boldsymbol{{sir}}! \\ $$

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