Question

Give the sumtotal of all odd numbers between 2 to 100

Answer 1

Heya user,

We have to find --> [ 3 + 5 + ... + 99 ]

Hence, this is equal to ---> [ ( 2 + 1 ) + ... + ( 98 + 1 )
= [ 1 + 1 + ... + 49 times ] + [ 2 + 4 + ... + 98 ]
= 49*1 + 2 [ 1 + 2 + ... + 49 ]
= 49 + 2 [ 1225 ] 
= 49 + 2450 = 2499...

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Another soln. is --->

We know, the sum of 'n' odd integers = n²
So, here, [ 1 + 2 + ... + 99 ] - 1 = sum of 50 odd integers -1  = 50² - 1 
= 2500 - 1 = 2499

Hence, we get the result as 2499;

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Or else, we can use the formula for sum of AP where a = 3; c.d. = 2

Hence the sum of 49 terms = 49/2 * [ 2a + ( 49 - 1 )c.d. ]
= 49/2 * [ 6 + 48*2 ]
= 49 * [ 3 + 48 ] = 49 * 51 = 2499;

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