Write each sum using summation notation

12 + 22 + 32 + 42 + ⋯ + 10000^2

50,00,70,000

Step-by-step explanation:

The given sequence is Arithmetic Progression.

Arithmetic Progression is a sequence in which every two neighbor digits have equal distances.

Here first we will find the number of terms

For finding the nth term, we use formula

aₙ = a + (n - 1) d

where, aₙ = value of nth term

a = First term

n = number of term

d = difference

Now, In given sequence: 12, 22, 32, 42, ⋯, 100002

a = 12, d = 10, n = ? and aₙ = 100002

∴ 100002 = 12 + (n - 1) * (10)

⇒ 99990 = 10 (n - 1)

⇒ n = 10000

Now using the formula of Sum of Arithmetic Sequence,

Sₙ = n:2[2a + (n - 1) d]

⇒ Sₙ = (10000:2) [2 * 12 + 9999 * 10]

⇒ Sₙ = 5000 [ 24 + 99990]

⇒ Sₙ = 5000 * 100014 = 50,00,70,000