Question

The sum of infinite series, 5+ 5/6 +5/36 + ………

Answer 1

The sum of infinite series, $5+\frac{5}{6} +\frac{5}{36} .........$ is 6.

Step-by-step explanation:

Given:

A infinite series,$5+\frac{5}{6} +\frac{5}{36} .........$.

To Find:

The sum of a infinite series,$5+\frac{5}{6} +\frac{5}{36} .........$.

Concept Used:

A geometric series is the sum of an infinite number of terms which  have a constant ratio between successive terms.

Solution:

As given, a infinite series,$5+\frac{5}{6} +\frac{5}{36} .........$.

A infinite series  $5+\frac{5}{6} +\frac{5}{36} .........$

This is  a this geometric series.

The common ratio (q) of the geometric series  $q=\frac{(\frac{5}{6}) }{6}=\frac{1}{6}$.

First term (p) of the  geometric series p=5.

Since $|q|=\frac{1}{6} < 1$. It implies that the series converges to $\frac{p}{1-q}$.

The sum of this infinite geometric series $=\frac{p}{1-q}$

                                                                   $=\frac{5}{1-\frac{1}{6} }$

                                                                    $=\frac{5}{\frac{6-5}{6} }$

                                                                   $=\frac{5}{\frac{5}{6} }$

                                                                   $=6$

Thus,the sum of this infinite geometric series is 6.

#SPJ3

Answer 2

The given question is The sum of infinite series, 5+ 5/6 +5/36 + ………

we have to find the sum of the above series.

The given series is

$5 + \frac{5}{6} + \frac{5}{36} + .......$

The above series is a geometric series, It is the sum of the infinite number of terms which have a constant ratio between successive terms.

The successive term of one number is the next number lies to the given number.

As given, the infinite series is

$5 + \frac{5}{6} + \frac{5}{36} + .....$

As early obtained the given series is a geometric series.

The common ratio of this series is

$\frac{second \: term}{first \: term}$

$\frac{ \frac{5}{6} }{5} = \frac{5}{6} \times \frac{1}{5}$

the same numbers will get cancelled, then we get.

$\frac{1}{6} as \: the \: common \: ratio = r$

since

$|r| < 1$

It implies that the series is converges to

$\frac{p}{1 - r}$

where p is the first term 5.

Therefore, the sum of this infinite series is

$\frac{p}{1 - r} \\ \frac{5}{1 - \frac{1}{6} } \\ \frac{5}{ \frac{6 - 1}{6} } \\ = \frac{5}{ \frac{5}{6} } \\ = 5 \times \frac{6}{5} \\ = 6$

The final answer obtained is 6.

Therefore, the sum of the given infinite series is 6.

$5 + \frac{5}{6} + \frac{5}{36} + ....... = 6$

# spj3

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https://brainly.in/question/52198451?referrer=searchResults