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Verified answer
4) (i = 1 Sigma 15) ai = 30(i = 1 Sigma 15) (5ai + 6)
= 5 (i = 1 Sigma 15) ai + (i = 1 Sigma 15) 6
= 5 (30) + 6(15)
= 150 + 90
= 240
6) (n = 1 Sigma 50) [1/n - 1/(n + 1)]
= [1/1 - 1/2] + [1/2 - 1/3] + [1/3 - 1/4] + .... + [1/49 - 1/50] + [1/50 - 1/51]
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ....... + 1/49 - 1/50 + 1/50 - 1/51
= 1 - 1/51
= 50/51