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JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Sequences and Series

The sum

1^{2} - 2. 3^{2} + 3. 5^{2} - 4. 7^{2} + 5. 9^{2} - \dots\dots\dots + 15.2 9^{2}

is ______.

Answer: 6952

Solution

The

k

-th term is

(- 1)^{k + 1} k (2 k - 1)^{2}

for

k = 1

to

15.

Summing the eight positive terms at odd positions,

\sum_{m = 1}^{8} (2 m - 1) (4 m - 3)^{2} = 29856

, and the seven negative terms at even positions,

\sum_{m = 1}^{7} (2 m) (4 m - 1)^{2} = 22904

, their difference gives

29856 - 22904 = 6952.

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Integer answer

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