InterviewSolution
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InterviewSolution
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If |x|gt1,then sum of the series(1)/(1+x)+(2)/(1+x^(2))+(2^(2))/(1+x^(4))+(2^(3))/(1+x^(8))+"......"" upto n terms "oo is (1)/(x-lambda),then the value of lambda is |
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Answer» Solution :LET `P=lim_(N to oo)((1)/(1+x)+(2)/(1+x^(2))+(2^(2))/(1+x^(4))+""....." upto n terms ")` `=lim_(n to oo)sum_(r=0)^(n)((2^(r ))/(1+x^(2^(r )))+(2^(r ))/(1-x^(2^(r )))-(2^(r ))/(1-x^(2^(r ))))` `=lim_(n to oo)sum_(r=0)^(n)((2^(r+1))/(1-x^(2^(r+1)))-(2^(r ))/(1+x^(2^( r))))` `=lim_(n to oo)((2^(n+1))/(1-x^(2^(n+1)))-(1)/(1+x))` `=lim_(n to oo)((2^(n+1))/(1-x^(2^(n+1))))/((1)/(x^(2^(n+1))-1))-(1)/(1+x)=0-(1)/(1-x)` `=(1)/(x-1)=(1)/(x-lambda) "" [" given "]` `:.lambda=1`. |
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