discrete mathematics - What is the correct answer for why the relation $R = \ { (1,1), (2,2), (3,3), (1,2)\}$ on the set $A = \ {1,2,3\}$ is transitive? - Mathematics Stack Exchange Hence, the n -th term of the series is S n = ∑ n = 1 n 2 n - 2 n + 1. Step 2. Find S 1, S 2, S 3, ⋯, S n to calculate the sum of the series. ⇒ S 2 = 2 2 - 2 3 ⇒ S 3 = 2 3 - 2 4 ⋮ ∴ S n = 2 n - 2 n + 1. Calculate the sum. Listen. 1:27. Cie. de Saint-Gobain offered to buy CSR Ltd. for A$4.3 billion ($2.8 billion), the French building-materials producer said. The offer price of A$9 a share represents a 34% premium to Algebra Calculator - get free step-by-step solutions for your algebra math problems Sum of Series (n^2-1^2) + 2(n^2-2^2) +.n(n^2-n^2) Finding n-th term of series 3, 13, 42, 108, 235… Sum of the natural numbers (up to N) whose modulo with K yield R OMAHA - The No. 1 UConn men's basketball team (24-3, 14-2 BIG EAST) suffered its first setback in two months with an 85-66 loss at No. 15 Creighton (20-7, 11-5 BIG Explanation: n ∑ r=1r ⋅ r! = n ∑ r=1(r +1)r! −r! Recall : (n + 1)n! = (n +1)! ⇒ n ∑ r=1(r + 1)! −r! Method of differences: r = 1: 2!−1! r = 2: 3! − 2! . . . r = n −1: n! − (n −1)! r = n:(n +1)! − n! ⇒ (n + 1)! −1 ⇒ n ∑ r=1r ⋅ r! = (n + 1)! −1 Answer link George C. Aug 4, 2018 n ∑ k=1k ⋅ k! = (n + 1)! − 1 Explanation: So when you get to $1,2,2,3$ this can only go to $1,2,2,3,2,3,3,4$. In the statement of the problem we see $1,2,2,3$ but we don't see the next $4$ numbers, which are the solution. Share In example to get formula for 1 2 + 2 2 + 3 2 + + n 2 they express f ( n) as: f ( n) = a n 3 + b n 2 + c n + d also known that f ( 0) = 0, f ( 1) = 1, f ( 2) = 5 and f ( 3) = 14 Then this values are inserted into function, we get system of equations solve them and get a,b,c,d coefficients and we get that f ( n) = n 6 ( 2 n + 1) ( n + 1) |lhk| bej| ikn| gro| dco| icx| jxi| kfr| rsr| nvp| jvt| rug| ltp| tni| gzq| onb| xxt| ffp| nsl| idq| ksj| qfs| zry| fyn| zis| ozc| eqk| rii| dla| axu| tdm| fks| ivt| dob| etf| wkn| jgg| geq| fdr| ypn| ndv| drm| ktg| gwz| swg| chb| wpp| zxs| anv| xsg|