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- Question 5 Exercise 4.1
- nded form, $\sum_{k=0}^{\infty}\left(\dfrac{3}{2}\right)^k$ ====Solution==== \begin{align}\sum_{k=0}^{\infty}\left(\dfrac{3}{2}\right)^k&=\left(\dfrac{3}{2}\right)^0+\left(\dfrac{3}{2}\right)^1+\left(\dfrac{3}{2}\right)^2+\left(\dfrac{3}{2}\right)^3+\ldots \\ &=1+\df
- Question 5 and 6 Exercise 4.2
- e sequence $$\log a, \log (a b), \log \left(a b^2\right), \log \left(a b^3\right), \ldots$$ is an A.P. Also find its nth term. ====Solution==== We first find $n... b^{n-1}) \\ &=\log \left(\dfrac{a b^n}{a b^{n-1}}\right)\\ &=\log b. \end{align} We see that the differen... -p2 |< Question 3 & 4]]</btn></text> <text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4
- Question 15 Exercise 4.2
- dfrac{b^n}{a^n}=1\\ \implies &\left(\dfrac{b}{a}\right)^n=\left(\dfrac{b}{a}\right)^0\\ \implies &n=0.\end{align} If $a=b$, then from (3), we have \begin{alig... 2-p10 |< Question 14 ]]</btn></text> <text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4
- Question 1 Exercise 4.3
- d,$$ This gives $$a_{11}=3+10\left(-\dfrac{1}{3}\right)=-\dfrac{1}{3}$$ Assume $S_n$ represents the sum ... implies S_{11}&=\dfrac{11}{2}\left[3-\dfrac{1}{3}\right] \\ &=\dfrac{11}{2} \cdot \dfrac{9-1}{3} \\&=\dfr... \dfrac{44}{3}$. GOOD ====Go To==== <text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4
- Question 7 Exercise 4.2
- 1), we get \begin{align} &a_1+4\left(\dfrac{1}{3}\right)=3\\ \implies &a_1=3-\dfrac{4}{3}=\dfrac{5}{3}. \... -p3 |< Question 5 & 6]]</btn></text> <text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4
- Question 1 and 2 Exercise 4.1
- ce are $0,0,1,4$. ====Go To==== <text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4
- Question 3 and 4 Exercise 4.1
- -p1 |< Question 1 & 2]]</btn></text> <text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4
- Question 1 and 2 Exercise 4.2
- iven sequence is 38. ====Go To==== <text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4
- Question 3 and 4 Exercise 4.2
- -p1 |< Question 1 & 2]]</btn></text> <text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4
- Question 8 Exercise 4.2
- x4-2-p4 |< Question 7]]</btn></text> <text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4
- Question 9 Exercise 4.2
- x4-2-p5 |< Question 8]]</btn></text> <text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4
- Question 10 Exercise 4.2
- x4-2-p6 |< Question 9]]</btn></text> <text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4
- Question 11 Exercise 4.2
- 4-2-p7 |< Question 10]]</btn></text> <text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4
- Question 12 & 13 Exercise 4.2
- -2-p8 |< Question 11 ]]</btn></text> <text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4
- Question 14 Exercise 4.2
- |< Question 12 & 13 ]]</btn></text> <text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4