Math
posted by arzam
1.(A)(i)Show that 2+4+6+8+..+2n=n(n+1).
(ii)Find the sum of the first 200 even numbers.
(iii)Find the sum of the first 200 odd numbers.
(B)(i)Use the formula at the beginning of the question to find the sum of the first 2n natural numbers.
(ii)Find a formula, in its simplest form, for 1+3+5+7+9+...+(2n1)

Steve
using induction
if n=1, 2 = 1(2) = 2
assuming true for n=k,
check for n=k+1:
2+...+2k+2k+2
= k(k+1) + 2k+2
= k(k+1) + 2(k+1)
= (k+1)(k+2)
as desired.
1+3+5+...+(2n1) = n^2
Respond to this Question
Similar Questions

Math riddle
nine odd numbers have a sum of 243.find the sum of the first and last numbers in a set of numbers. hint:if three numbers when added equals twelve then represent it by adding n+()n+1. 
Math riddle
nine odd numbers have a sum of 243.find the sum of the first and last numbers in a set of numbers. hint:if three numbers when added equals twelve then represent it by adding n+()n+1. no one cares...durrr.... 
SUMS?
what is the sum of the first towo odd numbers? 
math
The sum of the first 5 natural numbers is 15 or (5)(6)/2. The sum of the first 21 natural numbers is 231=(21)(22)/2, and the sum of the first 30 numbers is 465. Use inductive reasoning to derive the formula for the sum of the first … 
Math
Find the sum of the first 35 consecutive odd numbers. What is the sum of the first 350 consective odd numbers? 
Math 130
Sum the first two odd numbers, then the first three, the first four, and so on. From these observations could you guess the sum of the first 100 odd numbers? 
Math
Sum the first two odd numbers, then the first three, the first four, and so on. From these observations could you guess the sum of the first 100 odd numbers? 
arithmetic
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term … 
arithmetic
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term … 
math
If two dice are rolled and their faces noted, find each of the following probabilities: a) the sum of the two dice is 8 b) both dice show even numbers c) the sum of the two dice is 8 OR both dice show even numbers d) the sum of the …