Math, asked by hridyajomon108, 6 months ago

2¹+2²+2³+2⁴+2⁵..+2⁹⁹
Which is unit place number?

Answers

Answered by Anonymous
17

Concept : -  UNITS DIGIT USING CYCLICITY

Every number after multiplying itself for a given number of times the same number gets repeated in the units place which we call cyclicity.

  Numbers                 cyclicity        

   0 , 1 , 5 , 6                    1                        

   2 , 3 , 7 , 8                    4

       4 , 9                          2

Solution : -

Here we have powers of digit 2 so units digits gets repeated with cyclicity 4 with power cycles as  2 , 4 , 8 , 6 .

units digit of 2¹ = 2

units digit of 2² = 4

units digit of 2³ = 8

units digit of 2⁴ = 6

units digit of 2⁵ = 2....

Total no. of terms = 99

no. of complete power cycles = 99/4 = 24

last three will have units digits of  2 , 4 , 8

so sum of units places of all the terms ,

⇒ S = 24 x ( 2 + 4 + 8 + 6 ) + 2 +4 + 8

⇒ S = 24 x ( 20) + 14

    ⇒S = 494

Hence the units place is 4

∴ units digit of the sum of the series  2¹+2²+2³+2⁴+2⁵_____+2⁹⁹ = 4

                                   

Answered by bhagathpm2007
0

Answer:

What is the digit in the unit place of 2⁹⁹. ?

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