If S = ∑ r = 1 80 r r 4 + r 2 + 1 , then the value of 6481 S 1000 is

Step-by-step solution

T r = 1 2 r 2 + r + 1 - r 2 - r + 1 r 2 + r + 1 r 2 - r + 1 = 1 2 1 r 2 - r + 1 - 1 r 2 + r + 1 = 1 2 1 r 2 - r + 1 - 1 r + 1 2 - r + 1 + 1 = 1 2 f r - f r + 1 S = Σ T r = ∑ r = 1 80 1 2 f α - f α + 1 = 1 2 f 1 - f 2 + f 2 - f 3 . . . . . . . . + f 80 - f 81 = 1 2 f 1 - f 81 = 1 2 1 - 1 8 1 2 - 81 + 1 = 1 2 1 - 1 6481 ⇒ 6481 S = 6480 2 = 324 0 = 6481 S 1000 = 3240 1000 = 3.2 4