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- Question 10 Review Exercise
- n 10 of Review Exercise of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... text {th }}$ term and the sum to $n$ terms of the series $1+(1+\dfrac{1}{2})+(1+\dfrac{1}{2}+\dfrac{1}{4})... s$ ====Solution==== The general term of the given series is: \begin{align} a_n&=1+\dfrac{1}{2}+\dfrac{1}{4
- Question 9 Review Exercise
- on 9 of Review Exercise of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... )===== Find the sum of the first $n$ terms of the series $3+7+13+21+31+\ldots$ ====Solution==== Using meth... od of differences to compute the sum of the given series. \begin{align} & a_2-a_1=7-3=4 \\ & a_3-a_2=13-7=... \ldots \\ & a_n-a_{n-1}=(n-1) \text { term of the series } \\ & 4,6,8, \ldots \end{align} Adding column wi
- Question 8 Review Exercise
- on 8 of Review Exercise of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... estion 8(i)===== Find the sum of $n$ terms of the series whose $n^{t h}$ term is $n^3+3^n.$ ====Solution==... stion 8(ii)===== Find the sum of $n$ terms of the series whose $n^{t h}$ term is $2 n^2+3 n$ ====Solution=... tion 8(iii)===== Find the sum of $n$ terms of the series whose $n^{t h}$ term is $n(n+1)(n+4)$ ====Solutio
- Question 7 Review Exercise
- on 7 of Review Exercise of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... tan. =====Question 7(i)===== Find the sum of the series: $1.2^2+3.3^2+5.4^2+\ldots$ to $n$ terms. ====Solution==== The given series if the product of corresponding terms of the two series $1,3,5, \ldots,(2 n-1)$ and $2^2, 3^2, 4^2, \ldot
- Question 4 Review Exercise
- on 4 of Review Exercise of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... Peshawar, Pakistan. =====Question 4===== Sum the series: $\dfrac{1}{1.4 .7}+\dfrac{1}{4.7 .10}+\dfrac{1}{... nce $1,4,7, \ldots$ Thus the general term of the series is: $$a_n=\dfrac{1}{(3 n-2)(3 n+1)(3 n+4)}$$ Reso
- Question 5 & 6 Review Exercise
- & 6 of Review Exercise of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... Peshawar, Pakistan. =====Question 5===== Sum the series: $5+12 x+19 x^2+26 x^3+\ldots$ to $n$ terms. ====... {1-x}\\ \end{align} =====Question 6===== Sum the series: $\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\l... ===Solution==== Solution: The general term of the series is: $$T_n=\dfrac{1}{n(n+1)}$$ Resolving $T_n$ int
- Question 2 & 3 Review Exercise
- & 3 of Review Exercise of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... Peshawar, Pakistan. =====Question 2===== Sum the series to $n$ terms $1.2+2.3+3.4+\ldots$ ====Solution===... n+2)}{3}\end{align} =====Question 3===== Sum the series: $1.3 .5+2.4 .6+3.5 .7+\ldots$ to $n$ terms. ====Solution==== In the given series each term is the product of corresponding terms o
- Question 1 Review Exercise 5
- n+11$</collapse> ii. The sum to infinity of the series: $1+\dfrac{2}{3}+\dfrac{6}{3^2}+\dfrac{10}{3^3}+\... llapsed="true">(c): $3$ </collapse> iii. Sum the series:$1+2.2+3.2^2+\cdots+100.2^{\prime \prime}$ * ... 100}+1$</collapse> iv. The $n^{t h}$ term of the series: $1.2+2.3+3.4+\ldots$ * (a) $n^2-n$ * %%... : $n^2+n$ </collapse> v. Sum of $n$ terms of the series whose $n^{t h}$ term is $1+2^n$ * (a) $n \
- Question 4 Exercise 5.4
- stion 4 of Exercise 5.4 of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... kistan. =====Question 4===== Find the sum of the series: $\sum_{k=1}^n \dfrac{1}{k^2+7 k+12}$ ====Solutio... align} Consider the $n^{\text {th }}$ term of the series $$u_n=\dfrac{1}{(n+3)(n+4)}$$ Resolving into part
- Question 2 & 3 Exercise 5.4
- n 2 & 3 of Exercise 5.4 of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... , Pakistan. =====Question 2===== Find sum of the series: $\sum_{k=1}^n \dfrac{1}{9 k^2+3 k-2}$ ====Soluti... -1)(3 k-2)} \end{align} The $n$ term of the above series is: $$u_n=\dfrac{1}{(3 k-1)(3 k+2)}$$ Resolving i... {align} =====Question 3===== Find the sum of the series: $\sum_{k=1}^n \dfrac{1}{k^2-k}$ ====Solution====
- Question 6 Exercise 5.3
- stion 6 of Exercise 5.3 of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... == Find $n$ term and sum to $n$ terms each of the series $28+32+52+152+652+\ldots$ ====Solution==== \begin
- Question 1 Exercise 5.3
- stion 1 of Exercise 5.4 of Unit 05: Mascellaneous series. This is unit of A Textbook of Mathematics for Gr... istan. =====Question 1(i)==== Find the sum of the series $\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\ld... $ terms. ====Solution==== The general term of the series is: $$T_n=\dfrac{1}{n(n+1)}$$ Resolving $T_n$ int... =\dfrac{n}{n+1} \end{align} Hence the sum of the series is: $$S_n=\dfrac{n}{n+1}$$ =====Question 1(ii)==
- Question 5 Exercise 5.3
- stion 5 of Exercise 5.3 of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... == Find $n$ term and sum to $n$ terms each of the series $3+9+21+45+93+189+\ldots$ ====Solution==== \begin
- Question 4 Exercise 5.3
- stion 4 of Exercise 5.3 of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... == Find $n$ term and sum to $n$ terms each of the series $3+5+11+29+83+245+\ldots$ ====Solution==== \begin
- Question 2 Exercise 5.3
- stion 2 of Exercise 5.3 of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... = Find $n$ term and sum to $n$ terms each of the series $4+14+30+52+80+114+\ldots$ ====Solution==== \begi