निम्नलिखित श्रेढियों का योग अनन्त तक ज्ञात करो -
(A) `(2)/(5)-(3)/(5^(2))+(2)/(5^(3))-(3)/(5^(4))+(2)/(5^(5))-(3)/(5^(6))+......` (दो श्रेढियों में तोड़ लो)
(B) `(1+(1)/(2^(2)))+((1)/(2)+(1)/(2^(4)))+((1)/(2^(2))+(1)/(2^(6)))+....,`
(C) `(4)/(7)-(5)/(7^(2))+(4)/(7^(3))-(5)/(7^(4))+ .....,`
(D) `(3)/(4)-(5)/(4^(2))+(3)/(4^(3))-(5)/(4^(4))+.....,`
(E) `(1)/(7)+(2)/(7^(2))+(1)/(7^(3))+(2)/(7^(4))+(1)/(7^(5))+(2)/(7^(6))+.....,`
(F) `1+(sqrt(2)-1)/(2sqrt(3))+(3-2sqrt(2))/(12)+(5sqrt(2)-7)/(24sqrt(3))+.....`

Answer

`(A)(7)/(24)(B)2(1)/(2)(C)(23)/(48)(D)(7)/(15)(E)(3)/(16)(F)(2sqrt(3))/(2sqrt(3)-sqrt(2)+1)`