227k views
0 votes
Evaluate (precalculus)

Evaluate (precalculus)-example-1
User Gladen
by
8.8k points

1 Answer

4 votes

Answer:

S∞ = 7 Option C

Explanation:

Given that:

∑21
((1)/(4) )^(i) i = 1 to ∞

We need to find the sum.

Firstly we will find the sequence

a₁ =
21((1)/(4) )^(1)  = ((21)/(4) )

a₂ =
21((1)/(4) )^(2)  = ((21)/(16) )

a₃ =
21((1)/(4) )^(3)  = ((21)/(64) )

a₄ =
21((1)/(4) )^(4)  = ((21)/(256) )

this sequence is geometric

So, we use sum of infinite terms

a =
(21)/(4)

r =
((21)/(16) )/((21)/(4) )  = (1)/(4)

The sum of infinite terms of a GP series

S∞ =
(a)/(1-r)

where a is first term

r is common ratio and 0<r<1

S∞ =
((21)/(4) )/(1 - (1)/(4) ) &nbsp;= ((21)/(4) )/((3)/(4) )

S∞ = 7

User Rbento
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories