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- Definitions: FSc Part 1 (Mathematics): PTB @fsc-part1-ptb
- b$. If $a,A,b$ are in $A.P$. If $d$ is the common difference of the $A.P$, then $A-a=d$ and $b-A=d$. Thus $A-a
- 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
- Atiq ur Rehman, PhD
- rg>, <[email protected]> **Field of Research:** Difference and functional equations, Real functions, Inequal... Y. Mehboob, Mean value theorems associated to the differences of Opial–type inequalities and their fractional ... convex functions and related results, Advances in Difference Equations, 2020:163, (2020), 1-18. 46. L. N. Mis... iated results in fractional calculus, Advanced in Difference Equations, 2019:152 (2019), 1-13. 44. G. Farid,
- 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) @math-11-kpk:sol
- 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
- Mathematics 10 (Science Group) @matric
- * perform operations in set union, intersection, difference, complement. * give formal proofs of the follow
- 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
- FSc Part 1 (KPK Boards) @fsc
- ries and its sum of $n$ terms. * know method of differences and its uses. * use the partial fraction to fi... = Chapter 10: Trigonometric Identities of Sum and Difference of Angles ===== === Objectives === After reading ... xpress the product of sines and cosines as sum or differences of sines and cosines. * express the sums or differences of sines and cosines as product. ===Download=== <
- 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