Tan4theta=2 then Tanthta=?
Answers
Answer:
Step-by-step explanation:
Problem 1
Let \displaystyle {a_n}a
n
be a finite arithmetic progression and k be a natural number. \displaystyle a_1=r < 0a
1
=r<0 and \displaystyle a_k=0a
k
=0. Find \displaystyle S_{2k-1}S
2k−1
(the sum of the first 2k-1 elements of the progression).
Problem 2
Solve the equation
\displaystyle 1+4+7+\dots + x = 9251+4+7+⋯+x=925
Problem 3
Let \displaystyle \{a_n\}_1^{100}{a
n
}
1
100
be an arithmetic progression with 100 elements. \displaystyle a_1=5a
1
=5, \displaystyle a_2=8a
2
=8 and so on. \displaystyle \{b_n\}_1^{100}{b
n
}
1
100
also has 100 elements, but \displaystyle b_1=3b
1
=3, \displaystyle b_2=7b
2
=7 and so on. Find how many common elements \displaystyle \{a_n\}{a
n
} and \displaystyle \{b_n\}{b
n
} have.
Problem 4
Let \displaystyle \{a_n\}{a
n
} be a non-constant arithmetic progression. \displaystyle a_1=1a
1
=1 and the following holds true: for any \displaystyle n \ge 1n≥1, the value of \displaystyle \frac{a_{2n}+a_{2n-1}+...+a_{n+1}}{a_n+a_{n-1}+...+a_1}
a
n
+a
n−1
+...+a
1
a
2n
+a
2n−1
+...+a
n+1
remains constant (does not depend on \displaystyle nn). Find \displaystyle a_{15}a
15