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- Question 1, Review Exercise 10 @math-11-kpk:sol:unit10
- 0 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat
- Question 1 Exercise 4.3 @math-11-kpk:sol:unit04
- ion==== Let $a_1$ be first term and $d$ be common difference of given A.P. Then \begin{align}&a_1=9 \\ &d=7-9... ion==== Let $a_1$ be first term and $d$ be common difference of given A.P. Then \begin{align}&a_1=3 \\ &d=\df
- Question 7 Exercise 4.2 @math-11-kpk:sol:unit04
- ion==== Let $a_1$ be first term and $d$ be common difference of A.P. As given \begin{align} &a_6+a_4=6 \\ \im
- Question 5 and 6 Exercise 4.2 @math-11-kpk:sol:unit04
- }}\right)\\ &=\log b. \end{align} We see that the difference of consecutive terms $d$ is constant, i.e. indepe
- Question 9 Review Exercise @math-11-kpk:sol:unit05
- 13+21+31+\ldots$ ====Solution==== Using method of differences to compute the sum of the given series. \begin{a... +5+14+41+\ldots$ ====Solution==== Using method of differences to compute the sum of the given series. \begin{a
- Question 3 Exercise 5.3 @math-11-kpk:sol:unit05
- +40+\ldots$ ====Solution==== We use the method of difference as: \begin{align} & a_2-a_1=10-4=6 \\ & a_3-a_2=1
- Unit 05: Miscellaneous Series (Solutions)
- rithmetico-geometric series. * Define method of differences. * Use this method to find the sum of $n$ terms of the series whose differences of the consecutive terms are either in arithmeti
- Question 10 Exercise 4.4 @math-11-kpk:sol:unit04
- n. =====Question 10===== Find two numbers if the difference between them is $48$ and their A.M exceeds their ... two numbers be $a$ and $b$ \\ Condition-$1$\\ The difference between them is $48$\\ Therefore, $$\quad a-b=48.
- Question 7 & 8 Exercise 4.3 @math-11-kpk:sol:unit04
- equence\\ with first term $a_1=1$, and the common difference $d=2$.\\ We know that: \begin{align}S_n&=\dfrac{n
- Question 8 & 9, Review Exercise 10 @math-11-kpk:sol:unit10
- 0 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat
- Question 6 & 7, Review Exercise 10 @math-11-kpk:sol:unit10
- 0 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat
- Question 2 and 3, Review Exercise 10 @math-11-kpk:sol:unit10
- 0 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat
- Question 4 & 5, Review Exercise 10 @math-11-kpk:sol:unit10
- 0 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat
- Question 5, Exercise 10.3 @math-11-kpk:sol:unit10
- 3 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat
- Question 5, Exercise 10.3 @math-11-kpk:sol:unit10
- 3 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat