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Grade 12Algebra

Sir please help me as soon as possible !!!!
Find the value of (1 + 1/3.2² + 1/5.2⁴ + 1/7.2^{6 +...............infinity}
a) log_e3
B) 1/2 ln 3
c) 1/2 log_e 3 - 1
d) ln 3 - 1

Ranjeet Gupta

7 Years agoGrade 12

1 Answer

Ranjeet Gupta

7 Years ago

log_e(1+x)= x - x^2/2 + x^3/3 - x^4/4....... [eq 1]

log_e(1-x)= - x - x^2/2 - x^3/3 - x^4/4........ [eqⁿ 2]

Subtracting eq 2 from eq 1,

log_e(l+x) /(1-x) = 2( x + x^3/3 + x^5/5 + x^7/7......)

And now we put x=1/2 from the question condition

Then log_e(3) = 2(1/2 + 1/3*2^3 + 1/5*2^5 + 1/7*2^7........)

= (1 + 1/3.2^2 + 1/5.2^4 + 1/7.2^6....)

......... Dividing by 2 on b.s

Hence correct ans. a) log_e (3)

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