Calculate the sum $2 + (- 2) + 2 + (- 2) + . . . . .$
If the number of terms is $15$

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Solution

Here we have to see the series
$2 + (- 2) + 2 + (- 2) + . . . . .$
we observe that if the number of terms are odd then it is $2$
Here we see that number of terms are $15$ which is even then the sum is $2$

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The sum of the series
$45^{2} - 43^{2} + 44^{2} - 42^{2} + 43^{2} - 41^{2} + 42^{2} - 40^{2} + \dots 15 t e r m s$ is

45^{2} - 43^{2} + 44^{2} - 42^{2} + 43^{2} - 41^{2} + 42^{2} - 40^{2} + \dots 15 terms

(45^{2} - 43^{2}) + (44^{2} - 42^{2}) + (43^{2} - 41^{2}) + \dots

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15

2 + 5 + 8 + . . .

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