91影视

Write the first three terms in each binomial expansion, expressing the result in simplified form. $$ \left(y^{3}-1\right)^{21} $$

find each indicated sum. $$ \sum_{i=3}^{7} 12 $$

Find the sum of each infinite geometric series. $$ 1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+\cdots $$

find each indicated sum. $$ \sum_{i=0}^{4} \frac{(-1)^{i}}{i !} $$

Find \(1+2+3+4+\cdots+100,\) the sum of the first 100 natural numbers.

In the Cambridge Encyclopedia of Language (Cambridge University Press, 1987), author David Crystal presents five sentences that make a reasonable paragraph regardless of their order. The sentences are as follows: 鈥� Mark had told him about the foxes. 鈥� John looked out the window. 鈥� Could it be a fox? 鈥� However, nobody had seen one for months. 鈥� He thought he saw a shape in the bushes. How many different five-sentence paragraphs can be formed if the paragraph begins with 鈥淗e thought he saw a shape in the bushes鈥� and ends with 鈥淛ohn looked out of the window鈥�?

You are dealt one card from a 52-card deck. Find the probability that you are not dealt a king.

Find the term indicated in each expansion. $$ (2 x+y)^{6} ; \text { third term } $$

Find the sum of each infinite geometric series. $$ 3+\frac{3}{4}+\frac{3}{4^{2}}+\frac{3}{4^{3}}+\cdots $$

Find the sum of each infinite geometric series. $$ 5+\frac{5}{6}+\frac{5}{6^{2}}+\frac{5}{6^{3}}+\cdots $$