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Sum of an Infinite Arithmetic Geometric Series - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Sum of an infinite AGP is considered one the most difficult concept.

  • 4 Questions around this concept.

Concepts Covered - 0

Sum of an infinite AGP

Sum of an infinite AGP

S∞ denotes the sum of an infinite AGP. This sum is a finite quantity if -1 < r < 1 

\\\mathrm{S_\infty=\mathit{a+(a+d)r+(a+2d)r^2+(a+3d)r^3......}}\;\;\;\;\;....(i)\\\mathrm{Multiply\;both\;side\;of\;eq\;(i)\;by\;'r'}\\\mathrm{\mathit{r}S_\infty=\mathit{ar+(a+d)r^2+(a+2d)r^3+(a+3d)r^4.......}}\;\;\;\;\;....(ii)\\\mathrm{Subtract\;eq\;(ii)\;from\;eq\;(i)}\\\mathrm{\mathit{(1-r)}S_\infty=\mathit{a+ \left (dr+dr^2+dr^3+..... \;\;upto\;\;\infty \right ) }}\\\mathrm{\Rightarrow \mathit{(1-r)}S_\infty=\mathit{a+\frac{dr}{1-r}}}\\\\\mathrm{\Rightarrow \mathbf{S_\infty=\mathit{\mathbf{\frac{a}{1-r}+\frac{dr}{(1-r)^2}}}}}

Study other Related Concepts

Sum of an Infinite Arithmetic Geometric Series Current Topic

Sequence And Series
Arithmetic Progression
Sum of n Terms of an AP
Arithmetic Mean in AP
Geometric Progression
Geometric Mean In GP
Sum To n Terms Of a GP
Harmonic Progression
Harmonic Mean in HP
Relation between A.M., G.M. and H.M.

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