es lls ew zeiflucifiib ons einiseen stigesber Show that for neN, (2n)! ' (r!)² ((n −r)!)² - 7=0 2n - (2) ³. n

Q: 5) — = [(-D)" (2-1)", when 12-1}<1. n=0

A: Introduction: A geometric series is a type of series which is in the form as follows:…

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Q: (7) In general, (SOT)CSnT.But, (SnT) + SnŤ.

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Q: 5. (a) If r23 = 0, prove that R₁ (23) = (23) = 712 + 7³1 01-23 = (1 - 12 - 13). 07.

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Q: 6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

A: Note: Given proof statement has a little mistake, I have proof the actual result. First i have…

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A: We have given

Q: 133. -Σ 2" Sn+ -(x + 2)" n=0

A: Consider the series, Rewrite this as Now take the constant outside,

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A: Given g(t)=ℒ-1e-3s-7

Q: Q:- Show thet B(n, n) B( n+on+=2 1-40

A: The solution is given as

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A: For every integer n≥1, the nth cyclotomic polynomial Φn is the monic polynomial whose complex roots…

Q: п(п + 1) 15. Verify that E-1k is equal to for the cases (a) 2 n = 2, (b) n = 8, and (c) n = 9.

A: We have to verify that ∑kk=1n=n(n+1)2 for the cases (a) n=2 (b) n=8 and (c) n=9

Q: If n(Ax B) = 620 and n(B) = 31, find n(A). n(A)= n(B)= @)(::;:233)5

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Q: a/2 2. Evaluate f[(e)i-2sin(t) j+3cos(1)k]dt

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Q: en-3h-S If y= show that day (on-3)* 2n-3

A: Given function is  y=ex^2-3x-52x-3                           ⋯1 To show:…

Q: Prove that πd/n n = nτ(n)/2.

A: your question has a silly mistake, it should be πd|n d = nτ(n)/2. supposeτ(n)=r , where r be the…

Q: Show that when |z +1| < 1,z² =1+£(n +1)(z+1)" n=1

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Q: On October 1, Ebony Ernst organized Ernst Consulting; on October 3, the owner contributed $84,470 in…

A: We will make a table for income statement

Q: If I (F14)- s²+1 SO is given by? a) V(s? + 1)³

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Q: * :The nth term formula for { 1,0,1,0,... } is 1-(-1)" 2. an = A₂ = An خيار 2 1 + (−1)" 2.

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Q: y'+3xeY = o 0.

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Q: 2 Find (5a" + 4a*) da 1

A: We can find the integration value as below

Q: 12 3 n +2 (b) 2 = 2 – 2n + ..+ 22 23 2n lia on intege

A: (b)  To prove : 12+222+323+.....+n2n=2-n+22n for all n≥1   For n=1,  LHS : 12 RHS : 2-1+22=12= LHS…

Q: 17. Let P1.Pn be positive real numbers such that P1+ + Pn=1. (a) Prove the following: @P² ≥ (ii)…

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Q: (15 – b) (9 – b) - z = 6. 6. För a = 1 och b + 3 saknar systemet lösningar. För a = 1 eller (4t) , y…

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Q: Show that if s(3) 4(q- _9−2+9(1+ 93 2(g-1) increasing or decreasing. For 3 > 0, q> 3

A: The given function is                               sβ=q-2+q1+4q-1qβ122q-1 where β&gt;0 and q&gt;3.…

Q: { - (2)*} |리 > 2 z – 2 |리 > 2 z + 2 |리 > 2 z – 2 |리 > 2 z – 2 3.

A: The given problem is to find in which complex expression the given term {-(2k)} will be obtained. We…

Q: (1 2 43) 32 1. IF A = THEN (A) (B) (X Y) Z W

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Q: Suppose X~N (μ,σ') then X – H - - N (0, 1) o2 O True O False

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Q: 3 - 4 fX = the value of X" is - 1 %3D

A: We have to find the value of X^n

Q: 5. For n ≥ 1, establish the formula (2n + 1)² = (4tn + 1)² – (4tn)².

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Q: Evaluate: (3 e + 9* – 7) dr =.

A: Given : ∫3e3x+9x-7dx

Q: 2. Evaluate L-T/2(-1-i√3)

A: To evaluate the expression L base-pi/2[(-1-i√3)], we need to first understand what this expression…

Q: (b) Prove that 32n²+1, for n ≥ 1.

A: The given inequality is 3n≥2n2+1, for n≥1. We have to prove this inequality.

Q: Find residue 1 Res₂=0 24 +4% 2 Res 2 = 1 ze 3 2³-1 of

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Q: 4(-1)" Σ 3) Estimate 2N 1 correct to one decimal place. N-1

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Q: (-1)" (n+ 2) 2n+1(n + 1) Compute the exact value of

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