The value of lim n → ∞ 1 + 2 - 3 + 4 + 5 - 6 + … + ( 3 n - 2 ) + ( 3 n - 1 ) - 3 n 2 n 4 + 4 n + 3 - n 4 + 5 n + 4 is

Step-by-step solution

The given limit lim n → ∞ 1 + 2 - 3 + 4 + 5 - 6 + … + ( 3 n - 2 ) + ( 3 n - 1 ) - 3 n 2 n 4 + 4 n + 3 - n 4 + 5 n + 4 can be expressed as, lim n → ∞ ∑ r = 1 n 3 r - 2 + 3 r - 1 - 3 r 2 n 4 + 4 n + 3 - n 4 + 5 n + 4 = lim n → ∞ ∑ r = 1 n 3 r - 1 2 n 4 + 4 n + 3 - n 4 + 5 n + 4 = lim n → ∞ 0 + 3 + 6 + 9 + … . n   t e r m s 2 n 4 + 4 n + 3 - n 4 + 5 n + 4 . . . . . . . ( 1 ) We know the sum of the nth term of A.P. is given by S n = n 2 2 a +