Answer:The first differences are 6,8,10,12,14. The second difference is 2. Therefore half of 2 is 1 so the first term is n^2. Subtract this from the sequence gives 5,8,11,14,17. The nth term of this sequence is 3n + 2. So the final formula for this sequence is n^2 + 3n...
This makes sense since the values do not settle down for diverging series (either increasing or decreasing); the sequence at infinity must never be zero. What is the nth term test for convergence? Now, what happens when the nth term test returns a value of zero?When...
The formula operates by multiplying the common difference d by the position of the term (n - 1) and then adding the result to the first term a. This effectively accounts for the increasing or decreasingtrend in the sequence, enabling us to calculate the desired term. Newton's Little Formula...
1. (a) Find the limit of the sequence with the general term a_ n = 3n^3/9n^3 + 1. (b) Show that the sequence, a_ n = 1/5n + 2 is decreasing. Find the general term of the sequences, starting wit...
If the nth partial sum of a \sum_{n = 1}^{\infty} a_n is S_n = 3 - n2^{-n}, find a_n and the \sum_{n = 1}^{\infty} a_n. Determine the nth term of the arithmetic sequence whose n-th partial sum is n^2 + 2n . (Hint: The nth ter...
SAFit2 has previously been applied in other studies and no toxicity was demonstrated with long-term treat- ment [46–48]. Concurrent injection of C Cl4 and SAFit2 reduced indicators of liver injury, including lower inten- sity of trichrome staining (Fig. 9a) and lower quantified ...
Error term of the mean value theorem for binary Egyptian fractions The integral part of a nonlinear form with a square, a cube and a biquadrate Meromorphic solutions of certain nonlinear difference equations Characterizations for the potential operators on Carleson curves in local generalized Morre...
Sum of (-1)^n (3^n x^(7n))/(factorial of n) from n = 0 to infinity. For the telescoping series, find a formula for the n^{th} term of the sequence of partial sums \left \{ S_n \right \}. Then evaluate \lim_{n\rightarrow \in...