Calculate the sum of the infinite series s(infinity)=20-10+

A. S(\infty)=40/3

Step-by-step explanation:

Step-by-step explanation:

we are given series as

S(infinity)=20-10+5-..

Firstly, we will check type of series

first term=20

second term=-10

third term =5

now, we can find common ratios

we can see that both ratios are equal

so, this is geometric series

we can use sum of infinite terms formula

where a is first term

a=20

r=-0.5

now, we can plug values

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°