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Question

If sum to infinity of series 35r+7r29r3+. is 14/9, find r.

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Solution

S=35r+7r29r3+..=149
rs=3r+5r2+7r2+..
s+rs=32r+2r22r3+...
s(1+r)=3+(2r)1r
149.(1+r)=3+(2r1r)
14+14r=9(3(1r))2r×9
14+14r=2727r18r
(14r+14)(1r)=2745r
14r14r2+1414r=2745r
14r2+45r13=0
14r245r+13=0
value of roots of this eqn

1142291_1143696_ans_d46f1ebddf8d4ef2901ac2c4b4059c8b.jpg

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