सिद्ध कीजिए की
` ( 1)/( 1.2) +( 1)/(3.4) +( 1)/( 5.6) + ..........` अनंत तक `=log _e2 `

Show that, log_e2=1/(1.2)+1/(3.4)+1/(5.6)+.....infty

सिद्ध कीजिए कि 2tan^(-1)sqrt((b)/(a))=cos^(-1)((a-b)/(a+b))

(1)/(log_(2) e) + (1)/(log_(2)e^(2)) + (1)/(log_(2) e^(4)) + .... =

Prove that, 1/(1.2)-1/(2.3)+1/(3.4)-.....=2log_e2-1

Prove that, 1/(2.3)-1/(4.5)+1/(6.7)+.....=1-log_e2

The series expansion of log_(e) [(1 + x^((1 + x))(1-x)^(1-x)] is (1) 2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (2) [(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (3) 2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...] (4) 2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]