aligned & If 1 1^4 + 1 2^4 + 1 3^4 + . . = ^4 90 , & 1 1^4 + 1 3^4 + 1 5^4 + . . = , & 1 2^4 + 1 4^4 + 1 6^4 + . = , aligned then is equal to

Step-by-step solution

If 1 1^4 + 1 2^4 + 1 3^4 + . . = ^4 90 ....(i) aligned & = 1 2^4 + 1 4^4 + 1 6^4 + , & = 1 16 [ 1 1^4 + 1 2^4 + 1 3^4 + . . ], aligned = 1 16 ^4 90 using (ii) ________...(ii) aligned & = 1 1^4 + 1 3^4 + 1 5^4 + . . & ( 1 1^4 + 1 2^4 + 1 3^4 + 1 4^4 + 1 5^4 + . . ) & - ( 1 2^4 + 1 4^4 + 1 6^4 + . . ) aligned = ^4 90 - 1 16 ^4 90 [ using (i) and (ii)] aligned & = 16-1 16 90 ^4= 15 16 90 ^4= ^4 96 & = ^4 96 ^4 16 90 = 16 90 96 =15 aligned