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- Question 1 Exercise 5.1
- Question 2 & 3 Exercise 5.1
- Question 4 & 5 Exercise 5.1
- Question 6 Exercise 5.1
- Question 7 & 8 Exercise 5.1
- Question 9 Exercise 5.1
- Question 1 Exercise 5.2
- Question 2 & 3 Exercise 5.2
- Question 4 & 5 Exercise 5.2
- Question 1 Exercise 5.3
- Question 2 Exercise 5.3
- Question 3 Exercise 5.3
- Question 4 Exercise 5.3
- Question 5 Exercise 5.3
- Question 6 Exercise 5.3
- Question 1 Exercise 5.3
- Question 2 & 3 Exercise 5.4
- Question 4 Exercise 5.4
- Question 1 Review Exercise 5
- Question 2 & 3 Review Exercise
- Question 4 Review Exercise
- Question 5 & 6 Review Exercise
- Question 7 Review Exercise
- Question 8 Review Exercise
- Question 9 Review Exercise
- Question 10 Review Exercise
Fulltext results:
- Question 1 Exercise 5.3
- ====== Question 1 Exercise 5.3 ====== Solutions of Question 1 of Exercise 5.4 of Unit 05: Mascellaneou... {1}{2.3}+\dfrac{1}{3.4}+\ldots$ to $n$ terms. ====Solution==== The general term of the series is: $$T_n=\dfrac{1}{n(n+1)}$$ Resolving $T_n$ into partial fractions $$\dfrac{1}{n(n... {1}{3.5}+\dfrac{1}{5.7}+\ldots$ to $n$ terms. ====Solution==== Here $n$ term of the series is: $u_n=\df
- Question 2 & 3 Exercise 5.4
- ====== Question 2 & 3 Exercise 5.4 ====== Solutions of Question 2 & 3 of Exercise 5.4 of Unit 05: Miscu... series: $\sum_{k=1}^n \dfrac{1}{9 k^2+3 k-2}$ ====Solution==== \begin{align}\text { Let } S_n&=\sum_{k=... ve series is: $$u_n=\dfrac{1}{(3 k-1)(3 k+2)}$$ Resolving into partial fractions $$\dfrac{1}{(3 k-1)(3 ... e get $$3 A+3 B=0\quad \text{and}\quad 2 A-B=1$$ Solving the above two equations for $A$ and $B$ we g
- Question 1 Exercise 5.1
- ====== Question 1 Exercise 5.1 ====== Solutions of Question 1 of Exercise 5.1 of Unit 05: Mascellaneous... ies $1^2+3^2+5^2+7^2+\ldots$ up to $n$ terms. ====Solution==== We see that each term of the given serie... 2+2^2)+(1^2+2^2+3^2)+\ldots$ up to $n$ terms. ====Solution==== In the given series, we see that $T_1=1^... ies $2^2+4^2+6^2+8^2+\ldots$ up to $n$ terms. ====Solution==== The $n^{t h}$-term of the series is: $T_
- Question 1 Exercise 5.2
- ====== Question 1 Exercise 5.2 ====== Solutions of Question 1 of Exercise 5.2 of Unit 05: Mascellaneou... ms the series $1.2+2.2^2+3.2^3+4.2^4+\ldots$. ====Solution==== Let \begin{align} & S_n=1.2+2.2^2+3 \cdo... terms the series $1+4 x+7 x^2+10 x^3+\ldots.$ ====Solution==== Let \begin{align} & S_n=1+4 x+7 x^2+10 x... terms the series $1+2 x+3 x^2+4 x^3+\ldots$. ====Solution==== Let \begin{align} & S_n=1+2 x+3 x^2+4 x^
- Question 5 & 6 Review Exercise
- ====== Question 5 & 6 Review Exercise ====== Solutions of Question 5 & 6 of Review Exercise of Unit 05:... : $5+12 x+19 x^2+26 x^3+\ldots$ to $n$ terms. ====Solution==== Let \begin{align}S_n&=5+12 x+19 x^2+26 x... {1}{2.3}+\dfrac{1}{3.4}+\ldots$ to $n$ terms. ====Solution==== Solution: The general term of the series is: $$T_n=\dfrac{1}{n(n+1)}$$ Resolving $T_n$ into p
- Question 8 Review Exercise
- ====== Question 8 Review Exercise ====== Solutions of Question 8 of Review Exercise of Unit 05: Miscull... the series whose $n^{t h}$ term is $n^3+3^n.$ ====Solution==== The $n^h$ term is: $$a_n=n^3+3^n$$ Takin... he series whose $n^{t h}$ term is $2 n^2+3 n$ ====Solution==== The $n^{t h}$ term is: $$a_n=2 n^2+3 n$... series whose $n^{t h}$ term is $n(n+1)(n+4)$ ====Solution==== The $n^{\text {th }}$ term is: \begin{al
- Question 4 Review Exercise
- ====== Question 4 Review Exercise ====== Solutions of Question 4 of Review Exercise of Unit 05: Miscull... dfrac{1}{4.7 .10}+\dfrac{1}{7.10 .13}+\ldots$ ====Solution==== In the denominator Each term is the prod... es is: $$a_n=\dfrac{1}{(3 n-2)(3 n+1)(3 n+4)}$$ Resolving into partial fractions \begin{align} \dfrac{1... $A+B+C=0 \quad 15 A+6 B-3 C=0$$ $$4 A+8 B-2 C=1$$ Solving these three equations for the constants $A, B
- Question 2 & 3 Exercise 5.1
- ====== Question 2 & 3 Exercise 5.1 ====== Solutions of Question 2 & 3 of Exercise 5.1 of Unit 05: Miscu... an. Q2 Find the sum $1.2+2.3+3.4+\ldots+99.100$. Solution: The given series is the product of the corr... d} $$ Q3 Find the sum $1^2+3^2+5^2+\ldots+99^2$. Solution: The each term of the given series is the sq... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-1-p1 |< Question 1 ]]</btn></text> <te
- Question 4 & 5 Exercise 5.1
- ====== Question 4 & 5 Exercise 5.1 ====== Solutions of Question 4 & 5 of Exercise 5.1 of Unit 05: Miscu... the $2+(2+5)+(2+5+8)+\ldots$ up to $n$ terms. ====Solution==== The general term of the sequence is: \be... 5===== Sum: $2+5+10+17+\ldots$ to $n$ terms. ====Solution==== First we reform the given series as: $$(... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-1-p2 |< Question 2 & 3 ]]</btn></text>
- Question 7 & 8 Exercise 5.1
- ====== Question 7 & 8 Exercise 5.1 ====== Solutions of Question 7 & 8 of Exercise 5.1 of Unit 05: Miscu... to $n$ terms: $1.5 .9+2.6 .10+3.7 .11+\ldots$ ====Solution==== The general term of the series is: $T_j=... terms, whose $n^{t h}$-term is $4 n^2+5 n+1$. ====Solution==== Taking summation of the general term of ... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-1-p4 |< Question 6 ]]</btn></text> <te
- Question 2 & 3 Exercise 5.2
- ====== Question 2 & 3 Exercise 5.2 ====== Solutions of Question 2 & 3 of Exercise 5.2 of Unit 05: Miscu... 2===== $1+3^2 x+5^2 x^2+7^2 x^3+\ldots, x<1$. ====Solution==== Let \begin{align} & S_{\infty}=1+3^2 x+5... rac{3}{8}+\dfrac{4}{16}+\dfrac{5}{32}+\ldots$ ====Solution==== The given series is the product of the c... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-2-p1 |< Question 1 ]]</btn></text> <te
- Question 4 Exercise 5.4
- ====== Question 4 Exercise 5.4 ====== Solutions of Question 4 of Exercise 5.4 of Unit 05: Miscullaneous... series: $\sum_{k=1}^n \dfrac{1}{k^2+7 k+12}$ ====Solution==== Let \begin{align}S_n &=\sum_{k=1}^n \dfr... erm of the series $$u_n=\dfrac{1}{(n+3)(n+4)}$$ Resolving into partial fractions $$\dfrac{1}{(n+3)(n+4)}=\dfrac{A}{n+3}+\dfrac{B}{n+4}$$ Solving the above equation for $A$ and $B$, we get $
- Question 2 & 3 Review Exercise
- ====== Question 2 & 3 Review Exercise ====== Solutions of Question 2 & 3 of Review Exercise of Unit 05:... the series to $n$ terms $1.2+2.3+3.4+\ldots$ ====Solution==== The $n^{\text {th }}$ term is: $$a_n=n(n... : $1.3 .5+2.4 .6+3.5 .7+\ldots$ to $n$ terms. ====Solution==== In the given series each term is the pro... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit05:Re-ex5-p1 |< Question 1 ]]</btn></text> <t
- Question 7 Review Exercise
- ====== Question 7 Review Exercise ====== Solutions of Question 7 of Review Exercise of Unit 05: Miscull... ies: $1.2^2+3.3^2+5.4^2+\ldots$ to $n$ terms. ====Solution==== The given series if the product of corre... ies: $3.1^2+5.2^2+7.3^2+\ldots$ to $n$ terms. ====Solution==== In the given series each term is the pro... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit05:Re-ex5-p4 |< Question 5 & 6 ]]</btn></text
- Question 9 Review Exercise
- ====== Question 9 Review Exercise ====== Solutions of Question 9 of Review Exercise of Unit 05: Miscull... $n$ terms of the series $3+7+13+21+31+\ldots$ ====Solution==== Using method of differences to compute t... st $n$ terms of the series $2+5+14+41+\ldots$ ====Solution==== Using method of differences to compute t... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit05:Re-ex5-p6 |< Question 8 ]]</btn></text> <t