Question

S=1+5 mũ 2 + 5 mũ 4 +...+ 5 mũ 200

Answer 1

\(S=1+5+5^2+5^3+...+5^{200}\)

\(\Rightarrow5S=5+5^2+5^3+5^4+...+5^{201}\)

\(\Rightarrow5S-S=\left(5+5^2+5^3+...+5^{201}\right)-\left(1+5+5^2+...+5^{200}\right)\)

\(\Rightarrow4S=5^{201}-1\)

\(\Rightarrow S=\frac{5^{201}-1}{4}\)

Answer 2

\(S=1+5^2+...+5^{200}\)

\(5S=5+5^3+...+5^{201}\)

\(5S-S=\left(5+5^3+...+5^{201}\right)-\left(1+5^2+...+5^{200}\right)\)

\(4S=5+5^{201}-1+5^2\)

\(4S=5^{201}+29\)

\(S=\frac{5^{201}+29}{4}\)

Answer 3

\(S=1+5^2+5^4+...+5^{200}\)
\(25S=5^2+5^4+5^6+...+5^{202}\)
\(\Rightarrow25S-S=5^{202}-1\)
\(\Leftrightarrow S=\frac{5^{202}-1}{24}\)

Answer 4

S = 1 + 5² + 5⁴ + ..... + 5²⁰⁰

S x 5² = 5² + 5⁴ + 5⁶ + ........ + 5²⁰⁰ + 5²⁰²

S = ( 5² + 5⁴ + 5⁶ + ..... + 5²⁰² ) - ( 1 + 5² + 5⁴ + .... + 5²⁰⁰ )

S = ( 5²⁰² - 1 ) : 5

Answer 5

mọi người chắc ko

Answer 6

Đọc kĩ đề trước khi làm nhé mọi người :v

Answer 7

S=1+5²+5⁴+...+5²⁰⁰

25S=(1+5²+5⁴+...+5²⁰⁰).25

25S=5²+5⁴+5⁶+...+5²⁰²

25S-S=(5²+5⁴+5⁶+...+5²⁰²)-(1+5²+5⁴+...+5²⁰⁰)

24S=1-5²⁰²

S=\(\frac{1-5^{202}}{24}\)

vậy S=\(\frac{1-5^{202}}{24}\)