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JEE Main202331 Jan 2023Evening ShiftMathematicsSequences and SeriesActual

The sum 1 2 - 2 . 3 2 + 3 . 5 2 - 4 . 7 2 + 5 . 9 2 - … . . + 15 . 29 2 is _____ .

Correct answer

0

Step-by-step solution

Given, S = 1 2 - 2 · 3 2 + 3 · 5 2 . . . . . . . . . . . . + 15 · 29 2 Now rewriting the above expression we get, S = 1 2 + 2 · 3 2 + 3 · 5 2 . . . . . . . . . . . . + 15 · 29 2 ⏟ S 1 - 2 2 · 3 2 + 4 · 7 2 . . . . . . . . . . . . + 14 · 27 2 ⏟ S 2 Now solving S 1 = 1 2 + 2 · 3 2 + 3 · 5 2 . . . . . . . . . . . . + 15 · 29 2 ⇒ S 1 = ∑ r = 1 15 r · 2 r - 1 2 ⇒ S 1 = ∑ r = 1 15 r · 4 r 2 + 1 - 4 r ⇒ S 1 = &#

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