Question

Find the sum of the series 1+2+4+… upto 9 terms?

Answer 1

Hint: Here the given question is of sequence and series, here we need to understand the basic concept of geometric expression, that is if the common ratio between the adjacent number of the series are same then the given series is of the geometric, and here we can see that the common ratio of adjacent term are same and is equal to 2.
Formulae Used: Sum of n terms of geometric series:
\[ \Rightarrow Sum = \dfrac{{a({r^n} - 1)}}{{r - 1}}\]
Where, a=first term, r= common ratio, n=number of terms

Complete step-by-step solution:
Here the given question is of geometric series, on solving we get:
Sum of n terms of the geometric series is given by:
\[ \Rightarrow Sum = \dfrac{{a({r^n} - 1)}}{{r - 1}}\]
Here for the given question:
\[
   \Rightarrow a = 1 \\
   \Rightarrow r = \dfrac{2}{1} = 2 \\
   \Rightarrow n = 9 \\
 \]
now putting the values in the formulae we get:
\[ \Rightarrow Sum = \dfrac{{1({2^9} - 1)}}{{2 - 1}} = \dfrac{{256 - 1}}{1} = 255\]
Here we got the final sum of the given series in the above question.
Additional Information: Here in the above question we recognize the series and then solve further according to the formulae of the geometric series. The standard procedure to recognize the given series is to see the similarities between the adjacent term and then compare with the series.

Note: In the question of sequence and series, we always have to consider about recognizing the series, sometime the given series may be of not any standard series like arithmetic or geometric then to solve such series we have to make formulas from our hand and thus solve further.