determine the series obtained by changing the initial value of the infinite series: n ! 2 n + 1.

Use comparison test to determine whether the series ∑ n=1 ∞ 2 n + 3 n 5 + 1 converges or diverges. => diverges or converges or cannot be determined..

Find the sum to n terms of the geometric series. 1 + 4 + 16 + 64 + ... => 1 / 3 (4 n - 1) or 4 n - 1 or n 2 [ 2 + ( n - 1 ) 3 ] or 1 / 3 (1 -..

Determine whether the series ∑ n=1 ∞ 6 ( 6 n - 3 ) ( 6 n + 3 ) is convergent or divergent. If it converges, then find the sum. => divergent or cannot be determined or convergent, 2 or convergent, 1..

Use the Alternating Series Test to determine whether the series ∑ n=1 ∞ ( - 1 ) n ( n + 1 ) 3 n is convergent or divergent. => divergent or convergent or neither convergent nor divergent..

Use the Integral Test to determine whether the series ∑ n=1 ∞ 3 n 2 n 3 + 8 is convergent or divergent. => oscillating or divergent or cannot be determined or convergent..

Use comparison test to determine whether the series ∑ n=1 ∞ n 2 + 3 n 4 + 8 converges or diverges. => neither converges nor diverges or diverges or converges or cannot be determined..

Use the Limit Comparison Test to determine whether the series ∑ n=1 ∞ 3 n 5 n + 2 is convergent or divergent. => convergent or divergent or cannot be determined..

Use the Alternating Series Test to determine whether the series ∑ n=1 ∞ cos ( n π ) n ( n + 1 ) 3 is convergent or divergent. => convergent or cannot be determined or neither converge..

First, the data of concentrations versus time is obtained by a suitable method. Then, the data is plotted as concentration versus time. From the resulting plot, the instantaneous rates are determined by drawing tangents to curve and then calculating their slopes. The reaction ra..

Sum to n terms of a geometric series is (5 n - 1). Find the 43 th term. => 5(5 42 ) or 5 4 3 5 4 2 or 4(5 42 ) or 5 43 - 1..