JEE Main2013MathematicsSequences and SeriesActual

The sum 3 1^2 + 5 1^2+2^2 + 7 1^2+2^2+3^2 + . upto 11-terms is:

Options

A7 2
B11 4
C11 2
D60 11

Correct answer

C. 11 2

Step-by-step solution

Given sum is aligned & 3 12 + 5 1^2+2^2 + 7 1^2+2^2+3^2 + . . & n th term = T _n & = 2 n+1 n(n+1)(2 n+1) 6 = 6 n(n+1) & or T _n=6 [ 1 n - 1 n+1 ] & S _n= & T _n=6 1 n -6 1 n+1 = 6 n n - 6 n+1 & =6- 6 n+1 = 6 n n+1 & S₁₁= 6 11 11+1 = 66 12 = 33 6 = 11 2 & aligned

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