Question

Find the exact value of the sums S1 and S2 clearly explaining each step of your reasoning. 1² 2² - 3² - 2 +1 + 24 + 2 * 34 +3 + 9992 – 998 10002 - 999 9994 +999 - 10004 + 1000 sz-itvz + 12 + v + vätva + + VT8+ Vizo + v120 + VIZI

Answer 1

Solution : - Consider 24+2 8443 gggu tggg 100ot Hooo Clearly sa to h² (nail nyth ne con In = n²nt} = (h²h+1) th nihti) nint) (h²h+1). 1 is using a3 th} = (9+h) (9²ab they th= ( 1 ) - ( 11 ) tnt nint) where at Hence the given series Sn=ti+tz+tzt ... ttut... t4000 a =1-%+/- %+/- (4 79 Too Loo oo Sn= 1001-b 1001 sn - 1000 lool Hence Sum of this series is cool e Tsi = 1ooo I ains]

Solution ir Consider Tuttt- + 1+12 72713 J3tty + I + 119 t o 5120 tu1121 Rationalization of equation we have S2 = /2-2 & Baita (1 +112) (12-1) W3+y)(13–113) + - + 21 -1120 (V121 + Vrec)(17 – V120 3-12 3-2 S2 = 12 + + 73-7 fo sn + V121 - TTRO S2 = Jist - S2 = 11-L T32=10) Hence sum of this series is 10 te 132 =20] Ans]