The value of `tan^(-1).(4)/(7) + tan^(-1).(4)/(19) + tan^(-1).(4)/(39) + tan^(-1).(4)/(67) ... oo` equals

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tan^(-1)((4)/(7))+tan^(-1)((1)/(7)) = tan^(-1)((7)/(9))

Find the value of 4 tan^(-1).(1)/(5) - tan^(-1).(1)/(70) + tan^(-1).(1)/(99)

tan^(-1)((4)/(7))-tan^(-1)((1)/(5))=tan^(-1)((1)/(3))

Find the value of 4tan^(-1)(1)/(5)-tan^(-1)(1)/(70)+tan^(-1)(1)/(99)

2tan^(-1)((1)/(5))+tan^(-1)((1)/(8))= tan^(-1)((4)/(7))

the value of 3tan^(-1)((1)/(4))+tan^(-1)((1)/(20))+tan^(-1)((1)/(1985))

The value of tan^(-1)((1)/(3))+tan^(-1)((2)/(9))+tan^(-1)((4)/(33))+tan^(-1)((8)/(129))+...n terms is:

tan^(-1)((3)/(4))+tan^(-1)((3)/(5))-tan^(-1)((8)/(19))=

tan^(-1) (1/5) + tan^(-1) (1/7) + tan^(-1) (1/3) + tan^(-1) (1/8) = π/4