If n is odd, then (1+3+5+7+... to n terms) is equal to (a) (n² + 1) (b) (n² - 1) (c) n² (d) (2n² + 1) tell the method
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If n is odd, then (1+3+5+7+... to n terms) is equal to (a) (n² + 1) (b) (n² - 1) (c) n² (d) (2n² + 1) tell the method
Sol.
We know that,In the given series,a = 1, d = 3 - 1 = 2 Sum of n numbers = n 2 [ 2 ( 1 ) + ( n − 1 ) d ] n2[2(1)+(n−1)d] = n 2 [ 2 + ( n − 1 ) 2 ] n2[2+(n−1)2] = n 2 [ 2 + 2 n − 2 ] n2[2+2n−2] = n 2 × 2 n n2×2n = n2 Hence, Option (C) is the correct option.
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