Question

S=2+2^1+2^2+2^3+2^4+2^5+.....+2^99+2^100

S*10

Answer 1

S=2+2^1+2^2+...+2^100

2S=2.(2+2^1+2^2+...+2^100)

2S=2^2+2^3+...+2^101

2S-S=(2^2+2^3+...+2^101)-(2+2^1+...+2^100)

S=2^101-2

Sx10=(2^101-2)x10

Answer 2

 S=2+2^1+2^2+2^3+2^4+2^5+.....+2^99+2^100

\(\Rightarrow\)2S = 4 + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + ...... + 2¹⁰⁰ + 2¹⁰¹

\(\Rightarrow\)2S - S =  ( 4 + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + ...... + 2¹⁰⁰ + 2¹⁰¹ ) - ( 2 + 2¹ + 2²+ 2³ + 2⁴ + 2⁵ +.....+ 2⁹⁹ + 2¹⁰⁰ )

\(\Rightarrow\)S = ( 4 + 2¹⁰¹ ) - ( 2 + 2¹ )

\(\Rightarrow\)S x 10 = 2¹⁰¹ x 10

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