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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 4 Exercise 5.3
- term and sum to $n$ terms each of the series $3+5+11+29+83+245+\ldots$ ====Solution==== \begin{align} & a_2-a_1=5-3=2 \\ & a_3-a_2=11-5=6 \\ & a_4-a_3=29-11=18 \\ & \text {... ... ... } \\ & \text {... ... ... } \\ & a_n-a_{n-1}=(\math... === <text align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-3-p3 |< Question 3 ]]</btn></t
- Question 4 & 5 Exercise 5.2
- ical series $5+\dfrac{7}{3}+\dfrac{9}{3^2}+\dfrac{11}{3^3}+\ldots$ ====Solution==== Let \begin{align} ... & S_{\infty}=5+\dfrac{7}{3}+\dfrac{9}{3^2}+\dfrac{11}{3^3}+\ldots.(i) \\ & \dfrac{1}{3} S_{\infty}=\dfrac{5}{3}+\dfrac{7}{3^2}+\dfrac{9}{3^2}+\dfrac{11}{3^3}+\ldots.(ii) \end{align} Subtracting the (ii... === <text align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-2-p2 |< Question 2 & 3 ]]</btn
- Question 8 Review Exercise
- =n(n+1)\dfrac{2(2n+1)+9}{6}\\ & =\dfrac{n(n+1)(4n+11)}{6}\end{align} Thus sum to $n$ terms is: $$S_n=\dfrac{n(n+1)(4n+11)}{6}$$ =====Question 8(iii)===== Find the sum of... === <text align="left"><btn type="primary">[[math-11-kpk:sol:unit05:Re-ex5-p5 |< Question 7 ]]</btn></... t> <text align="right"><btn type="success">[[math-11-kpk:sol:unit05:Re-ex5-p7|Question 9 >]]</btn></t
- Question 7 & 8 Exercise 5.1
- ion 7===== Sum to $n$ terms: $1.5 .9+2.6 .10+3.7 .11+\ldots$ ====Solution==== The general term of the ... === <text align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-1-p4 |< Question 6 ]]</btn></t... t> <text align="right"><btn type="success">[[math-11-kpk:sol:unit05:ex5-1-p6|Question 9 >]]</btn></tex
- Question 2 Exercise 5.3
- um to $n$ terms each of the series $4+14+30+52+80+114+\ldots$ ====Solution==== \begin{align} & a_2-a_1... === <text align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-3-p1 |< Question 1 ]]</btn></t... t> <text align="right"><btn type="success">[[math-11-kpk:sol:unit05:ex5-3-p3|Question 3 >]]</btn></tex
- Question 1 Exercise 5.3
- series $\dfrac{1}{2.5}+\dfrac{1}{5.8}+\dfrac{1}{8.11}+\ldots$ to infinity. ====Solution==== Here in th... product of two successive terms of the A.P 2,5,8,11,... Therefore, the general term of the series i... == <text align="right"><btn type="success">[[math-11-kpk:sol:unit05:ex5-4-p2|Question 2 & 3 >]]</btn><
- Question 1 Review Exercise 5
- _{n+1}=$ * %%(a)%% $6 n-1$ * (b) $6 n+11$ * %%(c)%% $6 n+6$ * (d) $6 n-5$ \\ <btn ... /btn><collapse id="a1" collapsed="true">(b): $6 n+11$</collapse> ii. The sum to infinity of the serie... == <text align="right"><btn type="success">[[math-11-kpk:sol:unit05:Re-ex5-p2|Question 2 & 3 >]]</btn>
- Question 1 Exercise 5.1
- s of the above, we get \begin{align}& \sum_{j=1}^{11} T_j=8 \sum_{j=1}^n j^3-12 \sum_{i=1}^n j^2 \\ & ... == <text align="right"><btn type="success">[[math-11-kpk:sol:unit05:ex5-1-p3|Question 2 & 3 >]]</btn><
- Question 2 & 3 Exercise 5.1
- === <text align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-1-p1 |< Question 1 ]]</btn></t... t> <text align="right"><btn type="success">[[math-11-kpk:sol:unit05:ex5-1-p3|Question 4 & 5 >]]</btn><
- Question 4 & 5 Exercise 5.1
- === <text align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-1-p2 |< Question 2 & 3 ]]</btn... t> <text align="right"><btn type="success">[[math-11-kpk:sol:unit05:ex5-1-p4|Question 6 >]]</btn></te
- Question 6 Exercise 5.1
- === <text align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-1-p3 |< Question 4 & 5 ]]</btn... t> <text align="right"><btn type="success">[[math-11-kpk:sol:unit05:ex5-1-p5|Question 7 & 8 >]]</btn><
- Question 2 & 3 Exercise 5.2
- === <text align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-2-p1 |< Question 1 ]]</btn></t... t> <text align="right"><btn type="success">[[math-11-kpk:sol:unit05:ex5-2-p3|Question 4 & 5 >]]</btn><
- Question 3 Exercise 5.3
- === <text align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-3-p2 |< Question 2 ]]</btn></t... t> <text align="right"><btn type="success">[[math-11-kpk:sol:unit05:ex5-3-p4|Question 4 >]]</btn></tex
- Question 5 Exercise 5.3
- === <text align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-3-p4 |< Question 4 ]]</btn></t... t> <text align="right"><btn type="success">[[math-11-kpk:sol:unit05:ex5-3-p6|Question 6 >]]</btn></tex
- Question 2 & 3 Exercise 5.4
- === <text align="left"><btn type="primary">[[math-11-kpk:sol:unit05:ex5-4-p1 |< Question 1 ]]</btn></t... t> <text align="right"><btn type="success">[[math-11-kpk:sol:unit05:ex5-4-p3|Question 4 >]]</btn></te