Kindly see ques no 44 and its solution too...they used a formula a = ar/1-r , i just want to know how this formula is derived i.e what is its origin because we use the formula for Infinite series sum of GP = a / 1-r so on. Thus, the sum of first 2 terms is 2", of first 3terms it is 3² and so on. For 1111111 terms it wouldbe 11111112 = 1234567654321. Option (d) is correct.43. The area of the first square would be 1024 sq cm. thewould give 512, the third one 256 andso on. The infinite sum of the geometric progression= 2048. Option (a) issecondsquare1024 + 512 + 256 + 128...correct.ara =-1-ror 1 – r = r orr = 1/2 a + ar= 36 or a44.= 24%3D24Required sum == 48. Option (a) is correct.1%3D245. The side of the first equilateral triangle being 8 units,the first area is 16v3 square units. The second areawould be 1/4 of area of largest triangle and so on. Jerry drew a square of sides 32 cmand then kept on drawing squares inside the squaresby joining the mid points of the squares. She con-tinued this process indefinitely. Jerry asked Tom todetermine the sum of the areas of all the squaresthat she drew. If Tom answered correctly then whatwould be his answer?5 and176.A.М.X?(а) 2048(c) 51244. The sum of the first two terms of an infinite geo-metric series is 36. Also, each term of the series isequal to the sum of all the terms that follow. Findthe sum of the series(b) 1024(d) 4096eir(а) 48(c) 72(b) 54(d) 96

Let the infinite geometric series be a, ar, ar2, ar3,....... where a is the first term and r is the…

44. The sum of the first two terms of an infinite geo- metric series is 36. Also, each term of the series is equal to the sum of all the terms that follow. Find the sum of the series (а) 48 (c) 72 (b) 54 (d) 96

44. The sum of the first two terms of an infinite geo- metric series is 36. Also, each term of the series is equal to the sum of all the terms that follow. Find the sum of the series (а) 48 (c) 72 (b) 54 (d) 96

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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please send handwritten solution for Q4
For the series 3 terms, S3. S3 = ∞ n=1 (-1)" 3n0.1 + 5 calculate the sum of the first Include several decimals in your answer. Now find a bound for the error. Terror] <
3) You may have noticed that the series representations for ex, sin x, and cos x look very similar. One of the most important results in complex analysis is the identity eix = cos x + i sin x where i = √-1 is the imaginary unit. Prove this identity using Maclaurin series. (Fun fact: When you plug in to this identity, you get Euler's formula: ei + 1 = 0, a formula that includes all of the most important numbers in math!)
Please answer fast
Could y'all help me out with this? I know we are supposed to find an inequality, solve the inequality, then use that to find s_n, then find the error, but I'm not sure where to start or what to do.
(please solve within 15 minutes I will give thumbs up)