Q)I f space sum from n equals 1 to infinity of c o t to the power of negative 1 end exponent open parentheses 2 plus fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction close parentheses equals tan to the power of negative 1 end exponent a comma t h e n space apostrophe a apostrophe space i s space e q u a l space t o
left parenthesis A right parenthesis 1 space space space left parenthesis B right parenthesis 2 space space space space left parenthesis C right parenthesis 3 space space space space left parenthesis D right parenthesis 4

Asked by araima2001 | 24th Mar, 2017, 07:55: PM

Expert Answer:

begin mathsize 16px style sum from straight n minus 1 to infinity of cot to the power of negative 1 end exponent open parentheses 1 plus fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction close parentheses space on space expansion space converges space to space 3.
So comma space using space cot to the power of negative 1 end exponent straight x equals tan to the power of negative 1 end exponent open parentheses 1 over straight x close parentheses
we space get
tan to the power of negative 1 end exponent open parentheses 1 third close parentheses equals tan to the power of negative 1 end exponent straight a
rightwards double arrow straight a equals 1 third
Dear space student space please space check comma space we space are space getting space straight a equals 1 third space which space is space not space in space the space options. end style

Answered by Sneha shidid | 25th Mar, 2017, 08:24: PM