Find the value of 20+21+22+23+ .......+50

1275

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190

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1085

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None of the above

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Solution

The correct option is C 1085
Given series is 20+21+22+23+ .......+50.
= (1+2+3+ ......+50) - (1+2+3+.....+19)
$∵$ Sum of first 'n' natural numbers is $\frac{n \times (n + 1)}{2}$
$∴$ (1+2+3+ ......+50) = $\frac{50 \times (50 + 1)}{2}$
= $25 \times 51$
= 1275
and (1+2+3+.....+19) = $\frac{19 \times (19 + 1)}{2}$
= 190
$\Rightarrow$ 20+21+22+23+ .......+50 = 1275 - 190
= 1085

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