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Category: Arithmetic

1-1-2-3-1-2-3-4-1-3-4-5-1-n-n-1-n-2-

Question Number 202251 by BaliramKumar last updated on 23/Dec/23 $$\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}×\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{2}×\mathrm{3}×\mathrm{4}}\:+\:\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}×\mathrm{5}}\:+\:…………..\:+\:\frac{\mathrm{1}}{\mathrm{n}\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{2}\right)}\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Commented by BaliramKumar last updated on 23/Dec/23 $$\frac{\mathrm{1}}{\mathrm{a}\left(\mathrm{a}+\mathrm{d}\right)\left(\mathrm{a}+\mathrm{2d}\right)}\:+\:\frac{\mathrm{1}}{\left(\mathrm{a}+\mathrm{d}\right)\left(\mathrm{a}+\mathrm{2d}\right)\left(\mathrm{a}+\mathrm{3d}\right)}\:+\:\:…….+\:\frac{\mathrm{1}}{\left\{\mathrm{a}+\left(\mathrm{n}−\mathrm{1}\right)\mathrm{d}\right\}\left\{\mathrm{a}+\mathrm{nd}\right\}\left\{\mathrm{a}+\left(\mathrm{n}+\mathrm{1}\right)\mathrm{d}\right\}}\:=\:? \\ $$ Commented by MATHEMATICSAM…

1-1-3-1-3-5-1-5-7-

Question Number 202123 by BaliramKumar last updated on 21/Dec/23 $$\frac{\mathrm{1}}{\mathrm{1}×\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{3}×\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{5}×\mathrm{7}}\:+\:……………\infty\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 21/Dec/23 $${t}_{{n}} =\frac{\mathrm{1}}{\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)} \\ $$$$\:\:\:\:\:{let}\:\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}=\frac{{a}}{\mathrm{2}{n}−\mathrm{1}}+\frac{{b}}{\mathrm{2}{n}+\mathrm{1}} \\ $$$$\:\:\:{a}\left(\mathrm{2}{n}+\mathrm{1}\right)+{b}\left(\mathrm{2}{n}−\mathrm{1}\right)=\mathrm{1}…

There-are-two-possible-routes-from-Zindhi-to-Katifa-One-route-is-through-Zindhi-Chadler-expressway-which-is-100km-and-the-other-is-through-Adfeti-and-Ngonu-covering-a-distance-of-80km-A-motorist-goi

Question Number 202086 by necx122 last updated on 20/Dec/23 $${There}\:{are}\:{two}\:{possible}\:{routes}\:{from} \\ $$$${Zindhi}\:{to}\:{Katifa}.\:{One}\:{route}\:{is}\:{through} \\ $$$${Zindhi}/{Chadler}\:{expressway}\:{which}\:{is} \\ $$$$\mathrm{100}{km}\:{and}\:{the}\:{other}\:{is}\:{through}\:{Adfeti}\:{and} \\ $$$${Ngonu}\:{covering}\:{a}\:{distance}\:{of}\:\mathrm{80}{km}.\:{A} \\ $$$${motorist}\:{going}\:{through}\:{the}\:{expressway} \\ $$$${can}\:{travel}\:\mathrm{10}{km}/{h}\:{faster}\:{than}\:{the}\:{one} \\ $$$${going}\:{through}\:{Adfeti}\:{and}\:{Ngonu},\:{and} \\…

A-man-travelled-from-town-A-to-B-a-distance-of-360km-He-left-A-one-hour-later-than-he-had-planned-so-he-decided-to-drive-at-5km-h-faster-than-his-normal-speed-in-order-to-reach-B-on-schedule-If-he

Question Number 202079 by necx122 last updated on 19/Dec/23 $${A}\:{man}\:{travelled}\:{from}\:{town}\:{A}\:{to}\:{B},\:{a} \\ $$$${distance}\:{of}\:\mathrm{360}{km}.\:{He}\:{left}\:{A}\:{one}\:{hour} \\ $$$${later}\:{than}\:{he}\:{had}\:{planned}\:{so}\:{he}\:{decided} \\ $$$${to}\:{drive}\:{at}\:\mathrm{5}{km}/{h}\:{faster}\:{than}\:{his} \\ $$$${normal}\:{speed},\:{in}\:{order}\:{to}\:{reach}\:{B}\:{on} \\ $$$${schedule}.\:{If}\:{he}\:{arrived}\:{B}\:{at}\:{exactly}\:{the} \\ $$$${scheduled}\:{time},\:{find}\:{the}\:{normal}\:{speed}. \\ $$ Answered…

Solve-by-computer-programming-a-b-amp-c-are-Prime-numbers-And-they-are-in-AP-and-d-is-common-difference-Example-a-b-c-d-3-5-7-2-Just-Next-Set-a-b-c-d-

Question Number 202058 by BaliramKumar last updated on 19/Dec/23 $$\mathrm{Solve}\:\mathrm{by}\:\mathrm{computer}\:\mathrm{programming} \\ $$$${a},\:{b}\:\&\:{c}\:{are}\:{Prime}\:{numbers}.\:\mathrm{And}\:\mathrm{they} \\ $$$$\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}\:\mathrm{and}\:\mathrm{d}\:\mathrm{is}\:\mathrm{common}\:\mathrm{difference} \\ $$$$\mathrm{Example}\:\left(\mathrm{a},\:\mathrm{b},\:\mathrm{c},\:\mathrm{d}\right)\:=\:\left(\mathrm{3},\:\mathrm{5},\:\mathrm{7},\:\mathrm{2}\right) \\ $$$$\:\mathrm{Just}\:\mathrm{Next}\:\mathrm{Set}\left(\mathrm{a},\:\mathrm{b},\:\mathrm{c},\:\mathrm{d}\right)\:=\:? \\ $$ Commented by BaliramKumar last updated…