If the sum of the first 20 terms of the series 4.1 4+3.1^2+1^4 + 4.2 4+3.2^2+2^4 + 4.3 4+3.3^2+3^4 + 4.4 4+3.4^2+4^4 + is m n , where m and n are coprime, then m+n is equal to :-

Step-by-step solution

aligned & _ r =1 ²⁰ 4 r 4+3 r ^2+ r ^4 & _ r =1 ²⁰ 4 r ( r ^2+ r +2 ) ( r ^2- r +2 ) & 2 _ r =1 ²⁰ ( 1 r ^2- r +2 - 1 r ^2+ r +2 ) & 2 ( 1 2 - 1 4 ) & 1 4 - 1 8 & 1 8 - 1 14 & ( 1 382 - 1 422 ) & =2 ( 1 2 - 1 422 ) & = 420 422 & = 210 211 & option (3) aligned