Questions

1. Question 1

   Find the sum of first 15 terms of the G.P., $1,\ \dfrac{1}{3},\ \dfrac{1}{9},\ \ldots$.

   SolutionTheory
2. Question 2

   The 3rd term of a G.P. is 16 and the 6th term is $-128$. Find the first term and the sum of the first seven terms.

   SolutionTheory
3. Question 3

   Sum to $n$ terms the series:

   (i)

   $0.2 + 0.22 + 0.222 + \cdots$

   (ii)

   $3 + 33 + 333 + \cdots$

   SolutionTheory
4. Question 4

   Sum to $n$ terms the series:

   (i)

   $1 + (a+b) + (a^2 + ab + b^2) + (a^3 + a^2b + ab^2 + b^3) + \cdots$

   (ii)

   $r + (1+k)r^2 + (1+k+k^2)r^3 + \cdots$

   SolutionTheory
5. Question 5

   Sum the series $2 + (1-i) + \left(\dfrac{1}{i}\right) + \cdots$ to 8 terms.

   SolutionTheory
6. Question 6

   Show that the ratio of the sum of first $n$ terms of a G.P. to the sum of terms from $(n+1)^{th}$ to $(2n)^{th}$ term is $\dfrac{1}{r^n}$, where $r$ is the common ratio of the G.P.

   SolutionTheory