Question

Express 10 square as the sum of odd consecutive natural numbers​

Answer 1

Step-by-step explanation:

100= 10 square = 1+3+5+7+9+11+13+15+17+19

Answer 2

Answer:

Step-by-step explanation:

Using Arithmetic Progression, we are going to express it.

Formula used: Sum of n odd numbers (odd or even or natural or whole, the answer is based on the difference between 2 successive terms in the series)

                             Sₓ = 1/2 x n[2a+(n-1)×d]

Series be 1,3,5,7,9,11... (odd numbers)

Total numbers n = 10

First number in the sequence a = 1

Difference between two successive terms d = 3-1 = 2

Sum of n odd numbers: Sₓ = 1/2 x n[2a+(n-1)×d]

                                     S₁₀ = 1/2 x 10[2(1)+(10-1)2]

                                     S₁₀ = 1/2 x 10[2+18]

                                     S₁₀ = 5(20)

                                     S₁₀ = 100

Hence, It is proved.