Write sigma notation 1681 256625 1nn4 Which summation repre

Write sigma notation. 16-81 + 256-625 +...+(-1)^nn^4 Which summation represents the sum? A. sum^n_k=2 (-1)^k-1k^4 B. sum^n_k=2 (-1)^k4k C. sum^n_k=2 (-1)^kk^4 D. sum^n_k=2 k^4

Solution

16 - 81 + 256 - 625 +----+ (-1)ⁿ n⁴

==> 2⁴ + (-1) 3⁴ + 4⁴ + (-1) 5⁴ + ---- + (-1)ⁿ n⁴

==> (-1)² 2⁴ + (-1)³ 3⁴ + (-1)⁴ 4⁴ + (-1)⁵ 5⁴ + ---- + (-1)ⁿ n⁴

==> _{[k = 2 to n]} (-1)^k k⁴

Hence Option C