Niech Sk oznacza sumę k początkowych wyrazów ciągu (an). Znajdź a1,a2,a10 , jeśli : a) Sk=4k-3 b) Sk=k^2-2k c) Sk= 2/k d) Sk = √k+2

a) a1 = S1 = 4*1 - 3 = 1 a2 = S2 - S1 = 4*2 - 3 - 1 = 4 a10 = S10-S9 = 4*10 - 3 - (4*9 -3) = (40-3)-(36-3) = 37 - 33 = 4 b) a1 = S1 = 1^2 - 2*1 = -1 a2 = S2 - S1 = 2^2 - 2*2 -(-1) = 1 a10 = S10-S9 = 10^2 - 2*10 - (9^2 - 2*9) = 100-20 - (81 -18) = 80 - 63 = 17 c) a1 = S1 = 2/1 = 2 a2 = S2-S1 = 2/2 - 2 = -1 a10 = S10-S9 = 2/10 - 2/9 = 18/90 - 20/90 = 2/90 = 1/45 d) a1 = S1 = √1 + 2 = 1 + 2 = 3 a2 = S2 - S1 = √2 + 2 - (√1 + 2) = √2 - 1 a10 = S1 -S9 = √10 + 2 - (√9 + 2) = √10 - √9 = √10 - 3