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  1. Given that 1 + 2 + 3 + .... x =
    x(x + 1)
    then 1 + 3 + 5 + ..... + 99 is equal to
    2

    1. 2250
    2. 2500
    3. 2525
    4. 3775
Correct Option: D

Given that ,

1 + 2 + 3 + ............. + x =
x(x + 1)
2

∴ 1 + 3 + 5 + ............. + 99 = ( 1 + 2 + 3 + 4 + 5 +.....100) – ( 2 + 4 + 6 +.....100)
Required answer =
100 × (100 + 1)
-
50 × (50 + 1)
22

Hence , Required answer = 5050 – 1275 = 3775



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