JEE Main20254 Apr 2025Morning ShiftMathematicsSequences and SeriesActual

1+3+5^2+7+9^2+ upto 40 terms is equal to

Options

A43890
B41880
C33980
D40870

Correct answer

B. 41880

Step-by-step solution

(1^2+5^2+9^2+ upto 20 terms )+(3+7+11+ ...upto 20 terms) aligned & = _ r =1 ²⁰(4 r -3)^2+ _ r =1 ²⁰(4 r -1) & = _ r =1 ²⁰(4 r -3)^2+(4 r -1) & =4 _ r =1 ²⁰ (4 r ^2-5 r +2 ) & =16 _ r =1 ²⁰ r ^2-20 _ r =1 ²⁰ r +8 _ r =1 ²⁰ 1=41880 aligned

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