Question

An infinite geometric series has 1 and 1/5 as its first two terms: 1, 1/5, 1/25, 1/125, . . . What is the sum, S, of the infinite series? A. 1/4 B. 1 C. 5/4 D. 1/25

Answer 1

hey buddy here is your answer by UDIT

sum of infinite series where common ratio is <1

is S=a/1-r

where a is first term and r is common ratio

then

here r =1/5 and a =1

so S=1/(1-1/5)=5/4

THANKS

Answer 2

Answer :

option c) 5/4 is the sum, S, of the infinite series.

Step-by-step explanation:

• A geometric collection is the sum of finite or limitless phrases of a geometrical series.
• For the geometric series a, ar, ar², ..., ar^n-1, ..., the corresponding geometric collection is a + ar + ar² + ..., ar^n-1 + ....
• We recognise that "collection" way "sum". In particular, the geometric collection way the sum of the phrases which have a not unusualplace ratio among each adjoining of them.
• There may be varieties of geometric collection: finite and limitless.

$s= a/1-r\\ s=1/1-(1/5)\\5/4$

An infinite geometric series is the sum of an infinite geometric sequence.

infinite geometric series is the sum of an infinite geometric sequence. This series would have no last term.

The general form of the infinite geometric series is a1 + a1r + a1r² + a1r³+…,

• where a1 is the first term and
• r is the common ratio.

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