sorry, this is not from continuity but i had to ask it........ the question is find the last four digits of the number 2+22+222+2222+.......30000 terms.

Asked by Sheetal M G | 25th Mar, 2013, 07:10: PM

Expert Answer:

Given, x = 2 + 22 + 222 + 2222 + ........ + 222...... up to 30000 terms

Units digit of x is 0.

Adding the digits at the units place, we get

2 + 2 + 2 +.......... 30000 times = 60000

Tens digit of is 8.

Adding the digits at the tens place and the carry, we get

2 + 2 + 2+ ...... 29999 times + 6000 = 2 × 29999 + 6000 = 65998

Hundreds digit of x is 5.

Adding the digits at the hundreds place and the carry, we get

2 + 2 + 2 + .......  29998 times + 6599 = 2 × 29998 + 6599 = 66595

Thousands digit of x is 9.

Adding the digits at the thousands place and the carry, we get

2 + 2 + 2 + ....... 29997 times + 6659 = 2 × 29997 + 6659 = 66653

Thus, the last four digits of x are 3580.

Answered by  | 26th Mar, 2013, 03:17: AM

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