2 years ago

A path for a new city park will connect the park entrance to Main Street, as shown to the right. The path

Mathematics

1 answer:

sweet-ann [11.9K]2 years ago

5 0

Main street is vertical to park entrance

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Find S^20 if the series 1 + 1.1 ..... is a (a) arithmetic (b) geometric

quester [9]

I'm guessing S^20 is actually referring to the 20th partial sum $S_{20}$ , with

$S_{20}=1+(1+1\times0.1)+(1+2\times0.1)+\cdots+(1+18\times0.1)+(1+19\times0.1)$

in the arithmetic case, and

$S_{20}=1+1.1+1.1^2+\cdots+1.1^{18}+1.1^{19}$

in the geometric case.

(a) Combining like terms, we have

$S_{20}=20+0.1(1+2+\cdots+18+19)$

and invoking the formula

$1+2+\cdots+(n-1)+n=\dfrac{n(n+1)}2$

we end up with

$S_{20}=20+0.1\dfrac{19\times20}2=39$

(b) Multiply $S_{20}$ by 1.1, then subtract this from $S_{20}$ :

$1.1S_{20}=1.1+1.1^2+1.1^3+\cdots+1.1^{19}+1.1^{20}$

$S_{20}-1.1S_{20}=-0.1S_{20}=1-1.1^{20}$
$\implies S_{20}=\dfrac{1.1^{20}-1}{0.1}\approx57.275$

7 0

2 years ago

PLEASE HELP!!

NeTakaya

Answer:

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Is 10/9 closer to 1,1/2,0

balandron [24]

$\dfrac{10}{9}=\dfrac{9+1}{9}=\dfrac{9}{9}+\dfrac{1}{9}=1\dfrac{1}{9} \ \textgreater \ 1\\\\therefore\\\\\dfrac{10}{9}\ is\ closter\ to\ 1$