2. What is the general term of 1, 3, 6, 10, 15? O 2n – 1 n^2 – 1 (n^2+1)/n O (n(n+1))/2

Q: In (5 – x) – In (5 + x) = -In 9

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Q: What are the first and last terms in the expansion of (5x + 4y)*?

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Q: 2(5) – 3(1 – 6) 1. Is even integer? 5 2. List all even integers between -6 and 6. 3. Is 124/6…

A: Four questions are given. The solution to the four questions are given below.

Q: ind witnesses to show that n^3 − 5n^2 − 4n is O(n^3).

A: In this question, order of polynomial can be found with the help of Big-O notation. Big-O Notation…

Q: Write the binomial expansion for (x+ 2y)*. (x + 2y)* =D

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Q: Find a formula for ¹ - 1²/ (²1) + 1² ( 2 ) -—- ... ₁ (2). (G) + (-) + I u

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Q: For an integer n > 1, how many decimal stings of length n begin or end with an even digit? 5(10)"-1…

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Q: Value of the 7th term in (2x + y)"?

A: Follow the procedure given below.

Q: If C₁ * x² = c(1) ²¹ + a₂ (1) ²³ t² is the complementary solution of the nonhomogeneous system 3…

A: If the nonhomogeneous system is x'=3-22-2x+-2tt4-1 If the complimentary solution is…

Q: "Co 34 "C, "C, "C; (-1)" "C, ,ne Nis equal to 10 14 (4n + 2) 2" n! 2"-n! () 3.5-7...(2n - 1)(2n +1)…

A: We have use binomial theorem  1-xn=nC0 - nC1 x + nC2 x2  + .........+(-1)n   nCn

Q: Find J 11x(14)* -1'dx

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Q: Evaluate In x x (4 - In² x) - In 14- In² x | +C - 2 In 14-In² x | +C 12 -dx In | x (4- In²x) | +C In…

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Q: If x is positive, the first negative term in the expansion of (1 + x)27/5 is (a) 5th term (b) 6th…

A: Introduction :

Q: for

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Q: 1) Write all the following as expansions : > 0.2 > V26 V35 (0.99)-4 V(4 – 2y)2 ,y<2 2х-1° 2

A: (a) 0.2answer(a)0.2=2100.2=15(b) (26)13 answer(b) using approximation to solve the cube rootput x=27…

Q: This will be (n+k-1)= 29+6-1 29 -¹1) = 34 29 = 278, 256.

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Q: Find a formula for ¹ - 1²/ ( 7 ) + 3² ( 2 ) - ··· + + (−1)n. 2+1(1).

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Q: 21. Given that 3x4.-(2x)³ 12x-² A. 9 B. 11 = = Ax". Find the sum of A and n. C. 13 D. 15

A: Please see the below picture for detailed solution.

Q: Find a formula for +(−1)n. (2). 1 1 ¹ – ²2 ( ² ) + ² ( 2 ) - -· ··- 1 n+1

A: To Find: A formula for .

Q: Prove Vn € N, 1 1 + 1 2 + 1 3 + + 11 2n - 1 + 2n ≥1+ n 2

A: Let's prove the given inequality step by step:Base Case (n=1):11≥1+12This is true, as 11=1 and…

Q: 1- x**! 1- x n+1 6 (x # 1) r=0

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Q: The 4th term in the expansion of (2x -3x 10 is 10 C4 (2a) (-3x)³ O 10 C4 (2a2) (-32)4 10 C (2)…

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Q: The 4th term in the expansion of (2x² – 3x)* is - 10 Ca (2r²)*(-3z)® O 10 C4 (2a²)°(–3x)“ O 10 C3…

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Q: What is the coefficient of ?^11?^13 in the expansion (−3?+4?)^24.

A: It is asked to find coefficient of x11.y13 in the expansion of (-3x+4y)24.

Q: (x³ + })*

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Q: Let M = Find formulas for the entries of M", where n is a positive integer. Hint: a formula such as…

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Q: e3x + 6 enx e(n+1)x = 1+ e® + 2 Sx n! (n+ 1)!

A: The given series is : eex=1+ex+e2x2+e3x6+·····+enxn!+en+1xn+1!   Let fx=ex The above function can be…

Q: 1. Suppose when using the Binomial Theorem an expansion turned out to be the expression as shown…

A: Formula for Binomial theorem: a+bn=an+nan-1b+nn-12!an-2b2+nn-1n-23!an-3b3+.....+bn Given expression:…

Q: Show that (n + 1)! > 2"+3, for n > 5.

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Q: In two or more complete sentences, explain how to find the third term of the expansion of (2x+y)4.

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Q: What is the coefficient of x4y2z6 in the expansion of (3x² + 2y + 3z3)6?

A: Apply binomial theorem and isolate the coefficient

Q: 2(5) – 3(1 – 6) Is even integer?

A: If an integer is divisible by 2, then it is called an even integer. For example, 2,4,6 etc. are even…

Q: If n = 12 m (me N), prove that "C₂ (2+√3)² "Co- - + "C4 (2+√√3)4 n "C6 (2+√3)6 ·+···=(-

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Q: (:)? /3 9. Which of the following is equal to (b) (–1)"-12·5., 3"n! 3.5-7..... (2n + 1) (Зп — 4)…

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Q: 10 Which term of the expansion of (x²+4) ¹º contains x 20 Term number contains x 20

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