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Question Number 45512 by Tawa1 last updated on 13/Oct/18
Calculate: (((2^4 + (1/4)) (4^4 + (1/4))(6^4 + (1/4))(8^4 + (1/4))(10^4 + (1/4))(12^4 + (1/4)))/((1^4 + (1/4))(3^4 + (1/4)) (5^4 + (1/4)) (7^4 + (1/4)) (9^4 + (1/4))(11^4 + (1/4))))
$$\mathrm{Calculate}:\:\:\:\frac{\left(\mathrm{2}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\:\left(\mathrm{4}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{6}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{8}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{10}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{12}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)}{\left(\mathrm{1}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{3}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\:\left(\mathrm{5}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\:\left(\mathrm{7}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\:\left(\mathrm{9}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{11}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)} \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 14/Oct/18
excellent...sir...
$${excellent}…{sir}… \\ $$
Commented by Meritguide1234 last updated on 14/Oct/18
Commented by Tawa1 last updated on 14/Oct/18
God bless you sir
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$
Commented by Tawa1 last updated on 14/Oct/18
God bless you sir
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$
Commented by Tawa1 last updated on 14/Oct/18
Sir, why do we take answer for ((12^4 + (1/4))/(11^4 + (1/4))) = 313 as the final answer.
$$\mathrm{Sir},\:\mathrm{why}\:\mathrm{do}\:\mathrm{we}\:\mathrm{take}\:\mathrm{answer}\:\mathrm{for}\:\:\frac{\mathrm{12}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}}{\mathrm{11}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}}\:\:=\:\mathrm{313}\:\:\mathrm{as}\:\mathrm{the}\:\mathrm{final}\:\mathrm{answer}. \\ $$
Commented by Meritguide1234 last updated on 14/Oct/18
thank you ...sir
$${thank}\:{you}\:…{sir} \\ $$
Commented by Meritguide1234 last updated on 14/Oct/18
see i multiply all the term by telescopic series
$${see}\:{i}\:{multiply}\:{all}\:{the}\:{term}\:{by}\:{telescopic}\:{series} \\ $$
Commented by Tawa1 last updated on 14/Oct/18
Please sir, show example of how you multiply. Sorry to be bothering you sir, i just want to understand how you multiply sir
$$\mathrm{Please}\:\mathrm{sir},\:\mathrm{show}\:\mathrm{example}\:\mathrm{of}\:\mathrm{how}\:\mathrm{you}\:\mathrm{multiply}.\:\mathrm{Sorry}\:\mathrm{to}\:\mathrm{be}\:\mathrm{bothering} \\ $$$$\mathrm{you}\:\mathrm{sir},\:\:\mathrm{i}\:\mathrm{just}\:\mathrm{want}\:\mathrm{to}\:\mathrm{understand}\:\mathrm{how}\:\mathrm{you}\:\mathrm{multiply}\:\mathrm{sir} \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 14/Oct/18
((2^4 +(1/4))/(1^4 +(1/4)))=(((2^2 +2+(1/2))(2^2 −2+(1/2)))/((1^2 +1+(1/2))(1^2 −1+(1/2)))) now see the red marked expression bothare same value ((5/2)) so they cancelled.. ((4^4 +(1/4))/(3^4 +(1/4)))=(((4^2 +4+(1/2))(4^2 −4+(1/2)))/((3^2 +3+(1/2))(3^2 −3+(1/2)))) again see red marked expfession cancelled (((25)/2)) thus resul obtained...
$$\frac{\mathrm{2}^{\mathrm{4}} +\frac{\mathrm{1}}{\mathrm{4}}}{\mathrm{1}^{\mathrm{4}} +\frac{\mathrm{1}}{\mathrm{4}}}=\frac{\left(\mathrm{2}^{\mathrm{2}} +\mathrm{2}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\mathrm{2}^{\mathrm{2}} −\mathrm{2}+\frac{\mathrm{1}}{\mathrm{2}}\right)}{\left(\mathrm{1}^{\mathrm{2}} +\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\mathrm{1}^{\mathrm{2}} −\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\right)} \\ $$$${now}\:{see}\:{the}\:{red}\:{marked}\:{expression}\:\:{bothare} \\ $$$${same}\:{value}\:\left(\frac{\mathrm{5}}{\mathrm{2}}\right)\:\:{so}\:{they}\:{cancelled}.. \\ $$$$\frac{\mathrm{4}^{\mathrm{4}} +\frac{\mathrm{1}}{\mathrm{4}}}{\mathrm{3}^{\mathrm{4}} +\frac{\mathrm{1}}{\mathrm{4}}}=\frac{\left(\mathrm{4}^{\mathrm{2}} +\mathrm{4}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\mathrm{4}^{\mathrm{2}} −\mathrm{4}+\frac{\mathrm{1}}{\mathrm{2}}\right)}{\left(\mathrm{3}^{\mathrm{2}} +\mathrm{3}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\mathrm{3}^{\mathrm{2}} −\mathrm{3}+\frac{\mathrm{1}}{\mathrm{2}}\right)} \\ $$$${again}\:{see}\:{red}\:{marked}\:{expfession}\:{cancelled} \\ $$$$\left(\frac{\mathrm{25}}{\mathrm{2}}\right) \\ $$$${thus}\:{resul}\:{obtained}… \\ $$
Commented by Tawa1 last updated on 14/Oct/18
Wow, i understand now sir.
$$\mathrm{Wow},\:\mathrm{i}\:\mathrm{understand}\:\mathrm{now}\:\mathrm{sir}. \\ $$
Commented by Tawa1 last updated on 14/Oct/18
God bless you sir
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

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