free math problem answers

Question 1 - Question: Answer: As n represents all positive integers, we have Multiplying the above terms of both sides respectively, we get Multiplying both sides of inequality by n!, we g..

The determinant of coefficients ..

From (1) and (2) (A + B) + C = A + (B + C) verify the associative la..

We have 3A - 2B = 3A+(-2)..

Let S n = 1+2+3+4+...+n This series is an A.P. Here a=1, d=1, l = t n = n 2. To find the sum to squares of first n natural numbers. or..

Adding vertically, ..

n t h term of (1,2,3,....) is n Subtracting (ii) from (i), we get ..

i) 1.2 + 2.4 + 3.8 +.... to n terms The n t h term of (1,2,3,....n) is n. The n t h term of (2,4,8,...) is The n t h term of the given series is n2 n Subtracting (ii) from (i), we have ..

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The arrangement is as shown in the figure, the boy X will have B 2 , B 3 as neighbours. The girl Y will have G 2 , G 3 as neighbours. The two boys B 2 , B 3 can be arranged in two ways. The two girls G 2 , G 3 can be arranged in two ways. Hence, the total number of arrangements = 2 x 2 = ..