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JEE Main202131 Aug 2021Evening ShiftMathematicsSequences and SeriesActual

If S = 7 5 + 9 5 2 + 13 5 3 + 19 5 4 + … , then 160 S is equal to .

Correct answer

0

Step-by-step solution

Given, if S = 7 5 + 9 5 2 + 13 5 3 + 19 5 4 + … … ∞   . . . i Dividing by 5 on both sides of series S 5 = 7 5 2 + 9 5 3 + 13 5 4 + 19 5 5 + … … ∞   . . . i i Subtracting equations i & i i S - S 5 = 7 5 + 9 5 2 + 13 5 3 + 19 5 4 + … … ∞ - 7 5 2 + 9 5 3 + 13 5 4 + 19 5 5 + … … ∞ 4 S 5 = 7 5 + 9 5 2 - 7 5 2 + 13 5 3 - 9 5 3 + 19 5 4 - 13 5 4 + … … ∞ 4 S 5 = 7 5 + 2 5 2 + 4 5 3 + 6 5 4 + 8 5 5 + … … &#873

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