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प्रश्न
From the pattern, we can say that the sum of the first n positive odd numbers is equal to the square of the n-th positive number. Putting that into formula:
1 + 3 + 5 + 7 + ... n = n2, where the left hand side consists of n terms.
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उत्तर
Observe the following pattern
1 + 3 = 22
1 + 3 + 5 = 32
1 + 3 × 5 + 7 = 42
and write the value of 1 + 3 + 5 + 7 + 9 + ... upto n terms.
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संबंधित प्रश्न
Find the square of the given number.
93
What will be the units digit of the square of the following number?
4583
Observe the following pattern
22 − 12 = 2 + 1
32 − 22 = 3 + 2
42 − 32 = 4 + 3
52 − 42 = 5 + 4
and find the value of
1112 − 1092
Observe the following pattern \[1^2 = \frac{1}{6}\left[ 1 \times \left( 1 + 1 \right) \times \left( 2 \times 1 + 1 \right) \right]\]
\[ 1^2 + 2^2 = \frac{1}{6}\left[ 2 \times \left( 2 + 1 \right) \times \left( 2 \times 2 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 = \frac{1}{6}\left[ 3 \times \left( 3 + 1 \right) \times \left( 2 \times 3 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 + 4^2 = \frac{1}{6}\left[ 4 \times \left( 4 + 1 \right) \times \left( 2 \times 4 + 1 \right) \right]\] and find the values :
12 + 22 + 32 + 42 + ... + 102
Which of the following number square of even number?
324
Which of the following number square of even number?
4489
Find the square of the following number:
425
Find a Pythagorean triplet in which one member is 12.
For every natural number m, (2m – 1, 2m2 – 2m, 2m2 – 2m + 1) is a pythagorean triplet.
A 5.5 m long ladder is leaned against a wall. The ladder reaches the wall to a height of 4.4 m. Find the distance between the wall and the foot of the ladder.
