cot^-2+cot^-8+cot^-18+_______upto n terms find the sum of this series.
Atul , 5 Years ago
Grade 12
Algebra> cot^-2+cot^-8+cot^-18+_______upto n terms...
1 Answers
Arun
Last Activity: 5 Years ago
firstly in such questions try to find pattern between numbers : here it is 2n2 and then try to express it in form of tan-1a – tan-1b
∑ cot-1 ( 2n2 ) = ∑ tan-1 ( 1/2n2 ) { from n=1 to infinity }
tan-1 ( 2/4n2 ) = tan-1 { (2n+1) – (2n - 1) \1 + (2n - 1)(2n+1) } …......................1
tan-1a - tan-1b = tan-1 {(a-b)/1 + a*b}
so equation 1 equals to tan-1 (2n+1) – tan-1 (2n-1)
so now the qauestion is ∑ {tan-1 (2n+1) – tan-1 (2n-1) } [ n from 1 to infinity]
so now the answer is ( 
/2 – /4 ) = /4
Regards
Arun
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