1+ 1⁄2 + 1⁄4 + 1⁄8 + 1⁄16 + 1⁄32 + 1⁄64. . notice that the denominator of each fraction in the sum is twice the denominator that comes before it. if you continue adding on fractions according to this pattern, when will you reach a sum of 2?

Step-by-step explanation:

The given series is

This is a geometric series and the first term is

The common ratio is

The sum of the first n terms of this geometric series is given by,

We want to find such .

This implies that,

We simplify to get,

We multiply through by to get,

We group the constant terms to get,

This implies that,

We apply the laws of indices to further obtain,

We got division by zero, this means that  is infinity.

is the sum to infinity of the given series.

Hence we do not have a finite number of terms.

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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