1. Compute the following sums.a. 1+3+5+7+· +999b. 2+4+8+ 16+ · · + 1024...i(i + 1)h. Σ 1 1/i( + 1)c. +1 1d. S"+1Li=3Li=3iе.Li=03j+1f. Lj=l-j=1

Answered: a. 1+3+5+7+·+999 b. 2+4+8+ 16+ · ·+…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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1) Given series is Arithmetic Progression as difference between consecutive terms is constant.

nth term of A.P. is,

a_{n} = a_{1} + (n - 1) d

In given problem,

a_{n} = 999

a_{1} = 1

d = 3 - 1 = 2

∴ 999 = 1 + (n - 1) \times 2

∴ 998 = 2 (n - 1)

∴ n - 1 = 2 998

∴ n - 1 = 499

∴ n = 500

2) Sum of n terms of A.P. is

\sum a_{n} = 2 n [2 a + (n - 1) d]

∴ \sum a_{n} = 2 500 [(2 \times 1) + (500 - 1) \times 2]

∴ \sum a_{n} = 250 [2 + (499 \times 2)]

∴ \sum a_{n} = 250 [2 + 998]

∴ \sum a_{n} = 250 [1000]

∴ \sum a_{n} = 250000

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a. 1+3+5+7+·+999 b. 2+4+8+ 16+ · ·+ 1024

1) Given series is Arithmetic Progression as difference between consecutive terms is constant.