Question #c2066

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Answer 1 · 2017-03-21T11:55:50

#"The Sum="7776/2401~~3.23865.#

#"The Sum="sum_(n=5)^(oo)(6^n/7^n)#

#=sum_(n=5)^(oo) (6/7)^n#

#={(6/7)^5+(6/7)^6+(6/7)^7+..."(upto "oo)}#

#=(6/7)^5{1+(6/7)+(6/7)^2+... ...}#

Let us notice that the Series in #{... ... }# is a Geometric Series,

like, #{a+ar+ar^2+... ...}#, for which, the Sum #s# is given by,

#s=a/(1-r), iff r lt 1.#

Accordingly, in our Problem, #because, r=6/7 lt 1,#

#"The Sum="(6/7)^5{1/(1-(6/7))}=(6^5/7^5)(7)=6^5/7^4, or, #

#"The Sum="7776/2401~~3.23865.#

Enjoy Maths.!