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JEE Advanced Mathematics question

MathematicsSequence and SeriesJEE Advanced

Observe that

=1, =3+5, =7+9+11, =13+15+17+19.

Then as a similar series is

Answer: (C)

Solution

The first terms are , i.e. (check: for ). The th line has consecutive odd numbers starting from , so the last one is . Their sum is

Missing argument for \frac\frac -n+1)++n-1)]=Missing argument for \frac\frac n2ยท=.\

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Question ID VK-107857