910 Each of the following series is convergent. Find their sums. (a) n=2 (b) n=1 3 n²+7n+12 n=2 (5)" 4 (33) = 4 (())" = 4 (3)" 41号)=4(言 4(号) Geometric series Irl ====<| converges है n=2 ༢ 2 -(s) = 4 (2-1)) = 4 (4-5) = 4 (1/3) -1 =2 4 12++黒点 4(+) = 4 (1) --6 12+ (-6)+(-6)=0 3 b n=1 3 52+75+12 टै 3 3 B n=1 (n+3)(n+4) + (n+3)(n+4) 1+3 n+4. 3= A(n+4)+B (n+b) L>Let n=-4 3=B(-1) 3-B ↳ Let x=-3 3=A(-3+4) n= S= h+3 3 लग 4 - 一 3 n+4 5 52 = ( 2/4 - 2) + 15 512 20 3 = A 층) 5% -동) 12 20 له 2 लात 53 = ( 4 − 3 ) + ( ²² - 3) + (z - 3/3) 54 = ( ²² - } } ) + ( } } } ) + ( − 2 ) + ( 3 3 3 ) 3 3 SK = 4 TK+2 So this series converges to 30 20