Q.49 50145+5114434+52143342+53142343+... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q.49 (page 837)

$(\begin{matrix} 5 \\ 0 \end{matrix}) {(\frac{1}{4})}^{5} + (\begin{matrix} 5 \\ 1 \end{matrix}) {(\frac{1}{4})}^{4} (\frac{3}{4}) + (\begin{matrix} 5 \\ 2 \end{matrix}) {(\frac{1}{4})}^{3} {(\frac{3}{4})}^{2} + (\begin{matrix} 5 \\ 3 \end{matrix}) {(\frac{1}{4})}^{2} {(\frac{3}{4})}^{3} + (\begin{matrix} 5 \\ 4 \end{matrix}) {(\frac{1}{4})}^{1} {(\frac{3}{4})}^{4} + (\begin{matrix} 5 \\ 5 \end{matrix}) {(\frac{3}{4})}^{5} = ?$

Short Answer

Expert verified

The value of $(\begin{matrix} 5 \\ 0 \end{matrix}) {(\frac{1}{4})}^{5} + (\begin{matrix} 5 \\ 1 \end{matrix}) {(\frac{1}{4})}^{4} (\frac{3}{4}) + (\begin{matrix} 5 \\ 2 \end{matrix}) {(\frac{1}{4})}^{3} {(\frac{3}{4})}^{2} + (\begin{matrix} 5 \\ 3 \end{matrix}) {(\frac{1}{4})}^{2} {(\frac{3}{4})}^{3} + (\begin{matrix} 5 \\ 4 \end{matrix}) {(\frac{1}{4})}^{1} {(\frac{3}{4})}^{4} + (\begin{matrix} 5 \\ 5 \end{matrix}) {(\frac{3}{4})}^{5} = 1$

Step by step solution

Step 1. Given information

Here

$(\begin{matrix} 5 \\ 0 \end{matrix}) {(\frac{1}{4})}^{5} + (\begin{matrix} 5 \\ 1 \end{matrix}) {(\frac{1}{4})}^{4} (\frac{3}{4}) + (\begin{matrix} 5 \\ 2 \end{matrix}) {(\frac{1}{4})}^{3} {(\frac{3}{4})}^{2} + (\begin{matrix} 5 \\ 3 \end{matrix}) {(\frac{1}{4})}^{2} {(\frac{3}{4})}^{3} + (\begin{matrix} 5 \\ 4 \end{matrix}) {(\frac{1}{4})}^{1} {(\frac{3}{4})}^{4} + (\begin{matrix} 5 \\ 5 \end{matrix}) {(\frac{3}{4})}^{5} i s g i v e n$

we have to find out the value of the given statement

Step 2. Description of finding the value of given question

By using the binomial theorem we can find the value for this problem.

Binomial Theorem states that

$L e t x a n d a b e r e a l n u m b e r s . F o r a n y p o s i t i v e i n t e g e r n, w e h a v e {(x + a)}^{n} = (\begin{matrix} n \\ 0 \end{matrix}) x^{n} + (\begin{matrix} n \\ 1 \end{matrix}) a x^{n - 1} + (\begin{matrix} n \\ 2 \end{matrix}) a^{2} x^{n - 2} + . . . . . + (\begin{matrix} n \\ n \end{matrix}) a^{n} T h e g i v e n q u e s i o n (\begin{matrix} 5 \\ 0 \end{matrix}) {(\frac{1}{4})}^{5} + (\begin{matrix} 5 \\ 1 \end{matrix}) {(\frac{1}{4})}^{4} (\frac{3}{4}) + (\begin{matrix} 5 \\ 2 \end{matrix}) {(\frac{1}{4})}^{3} {(\frac{3}{4})}^{2} + (\begin{matrix} 5 \\ 3 \end{matrix}) {(\frac{1}{4})}^{2} {(\frac{3}{4})}^{3} + (\begin{matrix} 5 \\ 4 \end{matrix}) {(\frac{1}{4})}^{1} {(\frac{3}{4})}^{4} + (\begin{matrix} 5 \\ 5 \end{matrix}) {(\frac{3}{4})}^{5} i s g i v e n i s i n t h e f o r m o f b i n o m i a l t h e o r e m e x p a n s i o n . S o c o m p a r e d t o e x p a n d e d f o r m w e g e t n = 5, x = (\frac{1}{4}) a n d a = (\frac{3}{4}) t h e n b y a p p l y i n g b i n o m i a l e x p a n s i o n f o r m w e g e t {(\frac{1}{4} + \frac{3}{4})}^{5} = {(\frac{4}{4})}^{5} = {(1)}^{5} = 1, s o v a l u e o f (\begin{matrix} 5 \\ 0 \end{matrix}) {(\frac{1}{4})}^{5} + (\begin{matrix} 5 \\ 1 \end{matrix}) {(\frac{1}{4})}^{4} (\frac{3}{4}) + (\begin{matrix} 5 \\ 2 \end{matrix}) {(\frac{1}{4})}^{3} {(\frac{3}{4})}^{2} + (\begin{matrix} 5 \\ 3 \end{matrix}) {(\frac{1}{4})}^{2} {(\frac{3}{4})}^{3} + (\begin{matrix} 5 \\ 4 \end{matrix}) {(\frac{1}{4})}^{1} {(\frac{3}{4})}^{4} + (\begin{matrix} 5 \\ 5 \end{matrix}) {(\frac{3}{4})}^{5} i s 1$

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91影视

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Step by step solution

Step 1. Given information

Step 2. Description of finding the value of given question

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91影视

50145+5114434+52143342+53142343+54141344+55345=?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Description of finding the value of given question

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Applied Mathematics

Decision Maths

Mechanics Maths

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.