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Question Number 101418 by john santu last updated on 02/Jul/20

Find 2020 term from series  (1/1),(2/1),(1/2),(3/1),(2/2),(1/3),(4/1),(3/2),(2/3),(1/4)  ,(5/1),(4/2),... is ___  (A) ((2019)/(2020))      (B) ((61)/4)     (C)((63)/1)  (D) ((96)/4)      (E) ((2020)/(2019))

$$\mathrm{Find}\:\mathrm{2020}\:\mathrm{term}\:\mathrm{from}\:\mathrm{series} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}},\frac{\mathrm{2}}{\mathrm{1}},\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{3}}{\mathrm{1}},\frac{\mathrm{2}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{3}},\frac{\mathrm{4}}{\mathrm{1}},\frac{\mathrm{3}}{\mathrm{2}},\frac{\mathrm{2}}{\mathrm{3}},\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$,\frac{\mathrm{5}}{\mathrm{1}},\frac{\mathrm{4}}{\mathrm{2}},...\:\mathrm{is}\:\_\_\_ \\ $$$$\left(\mathrm{A}\right)\:\frac{\mathrm{2019}}{\mathrm{2020}}\:\:\:\:\:\:\left(\mathrm{B}\right)\:\frac{\mathrm{61}}{\mathrm{4}}\:\:\:\:\:\left(\mathrm{C}\right)\frac{\mathrm{63}}{\mathrm{1}} \\ $$$$\left(\mathrm{D}\right)\:\frac{\mathrm{96}}{\mathrm{4}}\:\:\:\:\:\:\left(\mathrm{E}\right)\:\frac{\mathrm{2020}}{\mathrm{2019}} \\ $$

Commented by PRITHWISH SEN 2 last updated on 02/Jul/20

2020=((4040)/2) = ((4032)/2) +4=((64×63)/2) + 4  =(((61+4−1)(61+4−2))/2)+4  i.e the term is ((61)/4) ans(B)   please check  sorry it was a typo

$$\mathrm{2020}=\frac{\mathrm{4040}}{\mathrm{2}}\:=\:\frac{\mathrm{4032}}{\mathrm{2}}\:+\mathrm{4}=\frac{\mathrm{64}×\mathrm{63}}{\mathrm{2}}\:+\:\mathrm{4} \\ $$$$=\frac{\left(\mathrm{61}+\mathrm{4}−\mathrm{1}\right)\left(\mathrm{61}+\mathrm{4}−\mathrm{2}\right)}{\mathrm{2}}+\mathrm{4} \\ $$$$\boldsymbol{\mathrm{i}}.\boldsymbol{\mathrm{e}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{term}}\:\boldsymbol{\mathrm{is}}\:\frac{\mathrm{61}}{\mathrm{4}}\:\boldsymbol{\mathrm{ans}}\left(\boldsymbol{\mathrm{B}}\right)\:\:\:\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{check}} \\ $$$$\mathrm{sorry}\:\mathrm{it}\:\mathrm{was}\:\mathrm{a}\:\mathrm{typo} \\ $$

Commented by bemath last updated on 02/Jul/20

why (((61+4−1)(61+4−2))/2)− 4 ?

$$\mathrm{why}\:\frac{\left(\mathrm{61}+\mathrm{4}−\mathrm{1}\right)\left(\mathrm{61}+\mathrm{4}−\mathrm{2}\right)}{\mathrm{2}}−\:\mathrm{4}\:? \\ $$

Commented by bramlex last updated on 02/Jul/20

what is the pattern on that series  sir?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{pattern}\:\mathrm{on}\:\mathrm{that}\:\mathrm{series} \\ $$$$\mathrm{sir}? \\ $$

Commented by RKT last updated on 03/Jul/20

I cannot tell you how he get the solution in 4 to 5 steps, but solution in two pages is here

Commented by RKT last updated on 03/Jul/20

Commented by RKT last updated on 03/Jul/20

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