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- Question 5 Exercise 4.1
- ing series in expanded 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)
- Question 5 and 6 Exercise 4.2
- how that the 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 ... a_n \\ &=\log (a b^n)-\log (a b^{n-1}) \\ &=\log \left(\dfrac{a b^n}{a b^{n-1}}\right)\\ &=\log b. \end{... ,19,24, \ldots$. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4
- Question 15 Exercise 4.2
- ^n \\ \implies &\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),... on is A.M for all $n$. ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4
- Question 7 Exercise 4.2
- value of $d$ in (1), we get \begin{align} &a_1+4\left(\dfrac{1}{3}\right)=3\\ \implies &a_1=3-\dfrac{4}... c{7}{3}, \ldots$. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4
- Question 1 Exercise 4.3
- hat $$a_n=a_1+(n-1) d,$$ This gives $$a_{11}=3+10\left(-\dfrac{1}{3}\right)=-\dfrac{1}{3}$$ Assume $S_n$... n}{2}[a_1+a_n], \\ \implies S_{11}&=\dfrac{11}{2}\left[3-\dfrac{1}{3}\right] \\ &=\dfrac{11}{2} \cdot \d
- Question 3 and 4 Exercise 4.1
- 2}, \dfrac{1}{8}$. ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4
- Question 6 Exercise 4.1
- ,0,0,0, \ldots$. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4
- Question 3 and 4 Exercise 4.2
- f given AP is 21. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4
- Question 8 Exercise 4.2
- in A.P. }\end{align} ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4
- Question 9 Exercise 4.2
- second is $3m$. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4
- Question 10 Exercise 4.2
- $ was $15135$. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4
- Question 11 Exercise 4.2
- top of the hill. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4
- Question 12 & 13 Exercise 4.2
- +b^2.\end{align} GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4
- Question 14 Exercise 4.2
- 0,23,26,29.$$ GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4
- Question 16 Exercise 4.2
- imes their A.M. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4