91Ó°ÊÓ

Use summation notation to write each series. Start the index at \(i=1\) $$\frac{1}{1+1}+\frac{2}{2+1}+\frac{3}{3+1}+\dots+\frac{25}{25+1}$$

Determine the largest value of \(n\) that satisfies the inequality. $$\sum_{i=1}^{n}(2 k-1)<26$$

Use summation notation to write each series. Start the index at \(i=1\) $$1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{9}$$

Find the future value of each annuity. Payments of \(\$ 1000\) at the end of each year for 9 years at \(2 \%\) interest compounded annually

Prove each statement for positive integers \(n\) and \(r\), with \(r \leq n\). (Hint: Use the definitions of permutations and combinations.) $$P(n, 0)=1$$

Prove each statement for positive integers \(n\) and \(r\), with \(r \leq n\). (Hint: Use the definitions of permutations and combinations.) $$C(n, n)=1$$

Find the future value of each annuity. Payments of \(\$ 800\) at the end of each year for 12 years at \(1 \%\) interest compounded annually

Use summation notation to write each series. Start the index at \(i=1\) $$-\frac{1}{3}+\frac{1}{9}-\frac{1}{27}+\frac{1}{81}-\dots-\frac{1}{2187}$$

Use a graphing calculator to graph the first 10 terms of each sequence. Make a conjecture as to whether the sequence comerges or diverges. If you think it converges, make a conjecture about the mumber to which it converges. $$a_{n}=\frac{n+4}{2 n}$$

Find the sum of all the integers from 51 to 71.