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- Question 1 Exercise 5.3
- KPTBB) Peshawar, Pakistan. =====Question 1(i)==== Find the sum of the series $\dfrac{1}{1.2}+\dfrac{1}{2... : $$S_n=\dfrac{n}{n+1}$$ =====Question 1(ii)==== Find the sum of the series $\dfrac{1}{1.3}+\dfrac{1}{3... ac{n}{2 n+1}\end{align} =====Question 1(iii)==== Find the sum of the series $\dfrac{1}{2.5}+\dfrac{1}{5... _{\infty}=\dfrac{1}{6}$$ =====Question 1(iv)==== Find the sum of the series $\dfrac{1}{4.13}+\dfrac{1}{
- Question 8 Review Exercise
- TBB) Peshawar, Pakistan. =====Question 8(i)===== Find the sum of $n$ terms of the series whose $n^{t h}... }+\dfrac{3}{2}(3^n-1)$$ =====Question 8(ii)===== Find the sum of $n$ terms of the series whose $n^{t h}... ac{n(n+1)(4n+11)}{6}$$ =====Question 8(iii)===== Find the sum of $n$ terms of the series whose $n^{t h}... )(3 n^2+23 n+34)}{12}$$ =====Question 8(iv)===== Find the sum of $n$ terms of the series whose $n^{t h}
- Question 2 & 3 Exercise 5.1
- ook Board (KPTB or KPTBB) Peshawar, Pakistan. Q2 Find the sum $1.2+2.3+3.4+\ldots+99.100$. Solution: Th... ldots+99.100 \\ & =3368050 . \end{aligned} $$ Q3 Find the sum $1^2+3^2+5^2+\ldots+99^2$. Solution: The ... erm of the series $1+3+5+\ldots+99$. So, first we find the total number of terms in the given series as:
- Question 9 Exercise 5.1
- TBB) Peshawar, Pakistan. =====Question 9(i)===== Find the sum of the $n$ terms of the series whose $n$-... }(n^2+3 n+1)\end{align} =====Question 9(ii)===== Find the sum of the $n$ terms of the series whose $n$-
- Question 4 & 5 Exercise 5.2
- KPTBB) Peshawar, Pakistan. =====Question 4===== Find the sum of the following arithtical geometrical s... s $3+5 r+7 r^2+\ldots \infty$ is $\dfrac{44}{9}$, find the value of $r$. ====Solution==== Let $$S_{\inft
- Question 2 & 3 Exercise 5.4
- KPTBB) Peshawar, Pakistan. =====Question 2===== Find sum of the series: $\sum_{k=1}^n \dfrac{1}{9 k^2+... rac{n}{2(3 n+2)}\end{align} =====Question 3===== Find the sum of the series: $\sum_{k=1}^n \dfrac{1}{k^
- Question 7 Review Exercise
- TBB) Peshawar, Pakistan. =====Question 7(i)===== Find the sum of the series: $1.2^2+3.3^2+5.4^2+\ldots$... 2+6 n-5)}{6}\end{align} =====Question 7(ii)===== Find the sum the series: $3.1^2+5.2^2+7.3^2+\ldots$ to
- Question 9 Review Exercise
- TBB) Peshawar, Pakistan. =====Question 9(i)===== Find the sum of the first $n$ terms of the series $3+7... ac{n(2 n^2+6 n+9)}{6}$$ =====Question 9(ii)===== Find the sum of the first $n$ terms of the series $2+5
- Question 4 & 5 Exercise 5.1
- KPTBB) Peshawar, Pakistan. =====Question 4===== Find the sum of the $2+(2+5)+(2+5+8)+\ldots$ up to $n$
- Question 7 & 8 Exercise 5.1
- 1)(n+8)(n+9)}{4}\end{align} =====Question 8===== Find the sum of the series upto $2 n$ terms, whose $n^
- Question 2 & 3 Exercise 5.2
- {8x^2}{(x-1)^3} \end{align} =====Question 3===== Find the $n^{\text {th }}$ term of the following arith
- Question 1 Exercise 5.3
- KPTBB) Peshawar, Pakistan. =====Question 1===== Find $n$ term and sum to $n$ terms each of the series
- Question 2 Exercise 5.3
- KPTBB) Peshawar, Pakistan. =====Question 2===== Find $n$ term and sum to $n$ terms each of the series
- Question 3 Exercise 5.3
- KPTBB) Peshawar, Pakistan. =====Question 3===== Find $n$ term and sum to $n$ terms each of the series
- Question 4 Exercise 5.3
- KPTBB) Peshawar, Pakistan. =====Question 4===== Find $n$ term and sum to $n$ terms each of the series