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ARITHMETIC PROGRESSIONS: One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories
Examples:
The fourth term of an AP is 0. Prove that its 25th term is triple its 11th term.
Ans: a4= 0
⇒ a + 3d = 0
T.P a25= 3 (a11)
⇒ a + 24d = 3 (a + 10d)
⇒ a + 24d = 3a + 30d
RHS sub a = - 3d
- 3d + 24d = 21d
LHS 3a + 30d
- 9d + 30d = 21d
LHS = RHS Hence proved
Children Learn By Experiencing Things : One view about learning says that children construct knowledge by acting upon things. They pick up things, throw them, break them, join the
Comparison Test or Limit Comparison Test In the preceding section we saw how to relate a series to an improper integral to find out the convergence of a series. When the inte
A regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual
Area with Parametric Equations In this section we will find out a formula for ascertaining the area under a parametric curve specified by the parametric equations, x = f (t)
even numbers
9w-w3
The King Company is producing two types of products: A and B. Both products are produced on the similar machining operation. The machines operate on two 8-hour shifts, 5 days per w
the value of square root of 200multiplied by square root of 5=
1. Use mathematical induction to prove whenever n is a positive integer. 2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.
A tower and a monument stand on a level plane. the angles of depression on top and bottom of the monument viewed from the top of the tower are 13 degrees and 31 degrees, respective
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