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Question Number 137403 by BHOOPENDRA last updated on 02/Apr/21

Commented by BHOOPENDRA last updated on 02/Apr/21

please help me out this in correct way

pleasehelpmeoutthisincorrectway

Answered by liberty last updated on 02/Apr/21

(1/(1.3)) +(1/(3.5))+(1/(5.7))+...= (1/3)+Σ_(n=1) ^∞ (1/((2n+1)(2n+3))) =(1/3)+lim_(n→∞) ((1/(3.5))+(1/(5.7))+(1/(7.9))+...+(1/((2n+1)(2n+3))) =(1/3)+lim_(n→∞) (1/2)[ ((5−3)/(3.5))+((7−5)/(5.7))+((9−7)/(7.9))+...+(((2n+3)−(2n+1))/((2n+1)(2n+3))) ] = (1/3)+lim_(n→∞) (1/2) [ (1/3)−(1/5)+(1/5)−(1/7)+(1/7)−(1/9)+...+(1/(2n+1))−(1/(2n+3)) ] =(1/3)+(1/2) lim_(n→∞) [ (1/3)−(1/(2n+3)) ] = (1/3)+(1/6)= (1/2)

11.3+13.5+15.7+...=13+∑∞n=11(2n+1)(2n+3)=13+limn→∞(13.5+15.7+17.9+...+1(2n+1)(2n+3)=13+limn→∞12[5−33.5+7−55.7+9−77.9+...+(2n+3)−(2n+1)(2n+1)(2n+3)]=13+limn→∞12[13−15+15−17+17−19+...+12n+1−12n+3]=13+12limn→∞[13−12n+3]=13+16=12

Commented by BHOOPENDRA last updated on 02/Apr/21

what about the upper part of the question sir

whatabouttheupperpartofthequestionsir

Commented by BHOOPENDRA last updated on 02/Apr/21

you have to express in I form

youhavetoexpressinIform

Commented by BHOOPENDRA last updated on 02/Apr/21

read the question again ,you are devlope f(x)as afourier series and then evaluate this f(x)=i(x)here

readthequestionagain,youaredevlopef(x)asafourierseriesandthenevaluatethisf(x)=i(x)here

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