Question

10. Find the sum by shortcut method: 1+2+3+97+98+99.​

Answer 1

SOLUTION

TO DETERMINE

The value of the sum by shortcut method

$\sf{1 + 2 + 3 + 97 + 98 + 99}$

EVALUATION

Here the given expression is

$\sf{1 + 2 + 3 + 97 + 98 + 99}$

We find the value by shortcut method as below

$\sf{1 + 2 + 3 + 97 + 98 + 99}$

$\sf{ = 1 + 2 + 3 + (100 - 3) + (100 - 2) + (100 - 1)}$

$\sf{ = 1 + 2 + 3 + 100 - 3 + 100 - 2 + 100 - 1}$

$\sf{ =100 + 100 + 100 + 1 + 2 + 3 - 1 - 2 - 3}$

$\sf{ =300+ 1 - 1 + 2 - 2 + 3 - 3}$

$\sf{ =300+ 0 + 0 + 0}$

$\sf{ =300}$

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Answer 2

Given : 1+2+3+97+98+99.​

To Find : sum by shortcut method

Solution:

1+2+3+97+98+99

using Commutative property   a + b = b + a

Hence changing the order

1 + 99 + 2 + 98  + 3 + 97

= ( 1 + 99) +  (2 + 98) + (3 + 97)

= 100 + 100 + 100​

= 300

1+2+3+97+98+99 = 300

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