সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=99$$ এবং সাধারণ অনুপাত: $$r=0.030303030303030304$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=99$$

$$a_2=a_1·r^{n-1}=99\cdot {0.030303030303030304}^{2-1}=99\cdot {0.030303030303030304}^1=99\cdot 0.030303030303030304=3$$

$$a_3=a_1·r^{n-1}=99\cdot {0.030303030303030304}^{3-1}=99\cdot {0.030303030303030304}^2=99\cdot 0.0009182736455463729=0.09090909090909093$$

$$a_4=a_1·r^{n-1}=99\cdot {0.030303030303030304}^{4-1}=99\cdot {0.030303030303030304}^3=99\cdot 2.7826474107465846E-05=0.0027548209366391185$$

$$a_5=a_1·r^{n-1}=99\cdot {0.030303030303030304}^{5-1}=99\cdot {0.030303030303030304}^4=99\cdot 8.432264881050256E-07=8.347942232239753E-05$$

$$a_6=a_1·r^{n-1}=99\cdot {0.030303030303030304}^{6-1}=99\cdot {0.030303030303030304}^5=99\cdot 2.5552317821364412E-08=2.529679464315077E-06$$

$$a_7=a_1·r^{n-1}=99\cdot {0.030303030303030304}^{7-1}=99\cdot {0.030303030303030304}^6=99\cdot 7.743126612534672E-10=7.665695346409325E-08$$

$$a_8=a_1·r^{n-1}=99\cdot {0.030303030303030304}^{8-1}=99\cdot {0.030303030303030304}^7=99\cdot 2.3464020037983852E-11=2.3229379837604015E-09$$

$$a_9=a_1·r^{n-1}=99\cdot {0.030303030303030304}^{9-1}=99\cdot {0.030303030303030304}^8=99\cdot 7.110309102419349E-13=7.039206011395156E-11$$

$$a_{10}=a_1·r^{n-1}=99\cdot {0.030303030303030304}^{10-1}=99\cdot {0.030303030303030304}^9=99\cdot 2.1546391219452575E-14=2.133092730725805E-12$$