Question

find the sum of the first 25 odd natural number​

Answer 1

(^O^)❤HEYY MATE❤


(^O^)❤HERE'S YOUR ANSWER❤


From 1 to 50 there are 50 natural numbers, half even and half odd, so we want the sum of the 25 odd numbers from 1 to 49. 

The sum S can be written forwards or backwards as: 

S = 1 + 3 + 5 + ........... + 45 + 47 + 49 or 
S = 49 +47 +45 + ............. + 5 + 3 + 1 

Notice that adding each vertical pair gives 50. 

How many 50s do we get? Looks like 25 of them which add up to 50 x 25 = 1250. But the 50s came from two of the sums S we want so we take half to get S = 625. 

Now can you find the sum of the first 100 odd numbers 
1 + 3 + 5 + ...... + 199 the same way? You should get 10,100. 



1 = 1^2 

1+ 3 = 4 = 2^2 

1+3+5 = 9 = 3^2 

1+3+5+7 = 16 = 4^2 

1+3+5+7+9 = 25 = 5^2 

leading you to guess (and prove later by induction) that 

1 + 3 + 5 + ..... 49 (first 25 odds) = 25^2 = 625. 

(^O^)❤HOPE THIS HELP SO❤

Answer 2

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