Question

for maths genius only !!!!!¡

can u solve question no. 22???​

Answer 1

Topic

Geometric Progression

Given

$nth \: term \: of \: a \: series \: is \: denoted \: by \: \sf{\dfrac{7^{n-1}}{10^n}}$

To Find

The sum to infinity of the series.

Concept

Sum of ∞ terms of a given Geometric Progression is [ a / 1 - r ].

where

• a = First Term
• r = Common Multiple

Solving

We will find some terms of given series and then observe the following terms.

So, putting n = 1 in formula gives

1 / 10

Now,

Putting n = 2 for second term, gives

7 / 100

Putting n = 3 for third term

49 / 1000

Similarly, we can do it for further terms.

Series :-

1/10, 7/100, 49/1000, 243/10000,............

We observe that to get next term, we need to multiply 7/10 to its previous term.

It means series forms a GP of common multiple 7/10.

Now,

Apply formula of Sum to infinite terms of a GP.

$Sum = \sf{\dfrac{a}{1 - r}}$

Here, a = 1 / 10 and r = 7 / 10.

$Sum = \sf{\dfrac{1/10}{1 - 7/10}}$

$Sum = \sf{\dfrac{1/{10}}{3/10}}$

Sum = 1 / 3

Answer

So, sum to infinite terms of given series

will be 1/3.

Learn More :-

Geometric Progression ( GP )

A series with a common multiple between its consecutive terms is known as GP.

For example :-

1, 2, 4, 8 , 16, ..........

Note :- The given formula for sum of infinite terms is only applicable when 'r' that is common multiple of GP is between 0 and 1.